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Lineare Funktionen/Station 4 - Versionsgeschichte
2024-03-29T06:15:54Z
Versionsgeschichte dieser Seite in ZUM-Unterrichten
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F.Bischof am 23. April 2022 um 15:41 Uhr
2022-04-23T15:41:28Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. April 2022, 15:41 Uhr</td>
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F.Bischof
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=122598&oldid=prev
Karl Kirst: - ZUM2Edutags
2021-12-17T11:06:13Z
<p>- ZUM2Edutags</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 17. Dezember 2021, 11:06 Uhr</td>
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Karl Kirst
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=80815&oldid=prev
Maria Eirich am 23. Dezember 2018 um 09:41 Uhr
2018-12-23T09:41:25Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 23. Dezember 2018, 09:41 Uhr</td>
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Maria Eirich
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=79170&oldid=prev
Kilian Schoeller am 4. Dezember 2018 um 08:28 Uhr
2018-12-04T08:28:42Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 4. Dezember 2018, 08:28 Uhr</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In diesem Abschnitt geht es darum, folgende Frage zu klären:<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In diesem Abschnitt geht es darum, folgende Frage zu klären:<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Frage|2=Eine lineare Funktion f hat die Steigung <math>m = 1,5</math> und verläuft durch den Punkt <math>A(2|0,5)</math>.<br><br> Wie würdest du vorgehen, um den Funktoinsterm der Funktion zu bestimmmen, <u>''ohne''</u> den Graphen zu zeichnen? <br>Dokumentiere deine Überlegungen im Schulheft.<br><br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Frage|2=Eine lineare Funktion <ins style="font-weight: bold; text-decoration: none;"><math></ins>f<ins style="font-weight: bold; text-decoration: none;"></math> </ins>hat die Steigung <math>m = 1,5</math> und verläuft durch den Punkt <math>A(2|0,5)</math>.<br><br> Wie würdest du vorgehen, um den Funktoinsterm der Funktion zu bestimmmen, <u>''ohne''</u> den Graphen zu zeichnen? <br>Dokumentiere deine Überlegungen im Schulheft.<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Du kommst nicht drauf? Oder bist dir nicht sicher? <br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Du kommst nicht drauf? Oder bist dir nicht sicher? <br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Lösung versteckt|1=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Lösung versteckt|1=</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*f ist linear, also gilt f(x) = m* x + t<br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins style="font-weight: bold; text-decoration: none;"><math></ins>f<ins style="font-weight: bold; text-decoration: none;"></math> </ins>ist linear, also gilt <ins style="font-weight: bold; text-decoration: none;"><math></ins>f(x) = m* x + t<ins style="font-weight: bold; text-decoration: none;"></math></ins><br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*f(x) = 1,5* x +t (Steigung ist ja gegeben)<br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins style="font-weight: bold; text-decoration: none;"><math></ins>f(x) = 1,5* x + t<ins style="font-weight: bold; text-decoration: none;"></math> </ins>(Steigung ist ja gegeben)<br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Wir müssen also im Endeffekt nur noch den y-Achsenabschnitt t bestimmen, oder?''<br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Wir müssen also im Endeffekt nur noch den y-Achsenabschnitt t bestimmen, oder?''<br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*A(2<del style="font-weight: bold; text-decoration: none;">{{!}}</del>0,5) liegt auf f, also f(2) = 0,5 und sowieso f(2) = 1,5 * 2 + t</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins style="font-weight: bold; text-decoration: none;"><math></ins>A(2<ins style="font-weight: bold; text-decoration: none;">|</ins>0,5)<ins style="font-weight: bold; text-decoration: none;"></math> </ins>liegt auf f, also <ins style="font-weight: bold; text-decoration: none;"><math></ins>f(2) = 0,5<ins style="font-weight: bold; text-decoration: none;"></math> </ins>und sowieso <ins style="font-weight: bold; text-decoration: none;"><math></ins>f(2) = 1,5 * 2 + t<ins style="font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Also: 1,5 * 2 + t = 0,5 oder kurz 3+t=0,5</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Also: <ins style="font-weight: bold; text-decoration: none;"><math></ins>1,5 * 2 + t = 0,5<ins style="font-weight: bold; text-decoration: none;"></math> </ins>oder kurz <ins style="font-weight: bold; text-decoration: none;"><math></ins>3+t=0,5<ins style="font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Damit: t=0,5-3 = -2,5<br><br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Damit: <ins style="font-weight: bold; text-decoration: none;"><math></ins>t = 0,5-3 = -2,5<ins style="font-weight: bold; text-decoration: none;"></math> </ins><br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktionsgleichung lautet: <math>f(x)=1,5\cdot x -2,5</math> }}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktionsgleichung lautet: <math>f(x)=1,5\cdot x -2,5</math> }}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Bestimmung der Funktionsgleichung|2=Wenn ein Punkt und die Steigung bekannt sind, kannst du die Funktionsgleichung bestimmen.<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Bestimmung der Funktionsgleichung|2=Wenn ein Punkt und die Steigung bekannt sind, kannst du die Funktionsgleichung bestimmen.<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Beispiel: Eine lineare Funktion <del style="font-weight: bold; text-decoration: none;">''</del>f<del style="font-weight: bold; text-decoration: none;">'' </del>hat die Steigung <math> m = 3</math> und verläuft durch den Punkt <math> A(1,4)</math>.<br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Beispiel: Eine lineare Funktion <ins style="font-weight: bold; text-decoration: none;"><math></ins>f<ins style="font-weight: bold; text-decoration: none;"></math> </ins>hat die Steigung <math> m = 3</math> und verläuft durch den Punkt <math> A(1,4)</math>.<br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>f ist linear, also f (x) = mx + t. Und da <math> m = 3</math> ist <math> f (x) = 3x + t </math><br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math></ins>f<ins style="font-weight: bold; text-decoration: none;"></math> </ins>ist linear, also <ins style="font-weight: bold; text-decoration: none;"><math></ins>f(x) = mx + t<ins style="font-weight: bold; text-decoration: none;"></math></ins>. Und da <math> m = 3</math> ist <math> f (x) = 3x + t </math><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Es muss nur noch t bestimmt werden!'''<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Es muss nur noch t bestimmt werden!'''<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>f (1) = 3 also 3*1 + t = 4 und damit t = 1</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math></ins>f(1) = 3<ins style="font-weight: bold; text-decoration: none;"></math> </ins>also <ins style="font-weight: bold; text-decoration: none;"><math></ins>3*1 + t = 4<ins style="font-weight: bold; text-decoration: none;"></math> </ins>und damit <ins style="font-weight: bold; text-decoration: none;"><math></ins>t = 1<ins style="font-weight: bold; text-decoration: none;"></math></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet somit : <math>f(x) = 3 x + 1</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet somit : <math>f(x) = 3 x + 1</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|3=Merksatz}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|3=Merksatz}}</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l53">Zeile 53:</td>
<td colspan="2" class="diff-lineno">Zeile 53:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Beispiel:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Beispiel:</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die lineare Funktion f verläuft durch die Punkte A(4<del style="font-weight: bold; text-decoration: none;">,</del>5) und B(-4<del style="font-weight: bold; text-decoration: none;">,</del>1).<br><br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die lineare Funktion f verläuft durch die Punkte <ins style="font-weight: bold; text-decoration: none;"><math></ins>A(4<ins style="font-weight: bold; text-decoration: none;">|</ins>5)<ins style="font-weight: bold; text-decoration: none;"></math> </ins>und <ins style="font-weight: bold; text-decoration: none;"><math></ins>B(-4<ins style="font-weight: bold; text-decoration: none;">|</ins>1)<ins style="font-weight: bold; text-decoration: none;"></math></ins>.<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Zunächst muss die Steigung m bestimmt werden!'''<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Zunächst muss die Steigung m bestimmt werden!'''<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> m=\frac{\Delta y}{\Delta x}=\frac{y_B-y_A}{x_B-x_A}=\frac{5-1}{4-(-4)}=\frac{4}{8}=0,5</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> m=\frac{\Delta y}{\Delta x}=\frac{y_B-y_A}{x_B-x_A}=\frac{5-1}{4-(-4)}=\frac{4}{8}=0,5</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Nun muss wie oben noch t bestimmt werden!''' Nehme entweder Punkt A oder B zu Hilfe.<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Nun muss wie oben noch t bestimmt werden!''' Nehme entweder Punkt A oder B zu Hilfe.<br><br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>f (x) = 0,5 x + t<br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math></ins>f(x) = 0,5 x + t<ins style="font-weight: bold; text-decoration: none;"></math></ins><br></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>f (4) = 5, also 0,5 * 4 + t = 5 und damit t = 3.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><math></ins>f(4) = 5, <ins style="font-weight: bold; text-decoration: none;">\text{ </ins>also <ins style="font-weight: bold; text-decoration: none;">} </ins>0,5 * 4 + t = 5 <ins style="font-weight: bold; text-decoration: none;">\text{ </ins>und damit <ins style="font-weight: bold; text-decoration: none;">} </ins>t = 3 <ins style="font-weight: bold; text-decoration: none;"></math></ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet: <math>f(x) = 0,5 x + 3</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet: <math>f(x) = 0,5 x + 3</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|3=Merksatz}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|3=Merksatz}}</div></td></tr>
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Kilian Schoeller
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=79119&oldid=prev
Kilian Schoeller am 3. Dezember 2018 um 11:05 Uhr
2018-12-03T11:05:55Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 3. Dezember 2018, 11:05 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l45">Zeile 45:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f (1) = 3 also 3*1 + t = 4 und damit t = 1</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f (1) = 3 also 3*1 + t = 4 und damit t = 1</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet somit : <math>f(x) = 3 x + 1</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet somit : <math>f(x) = 3 x + 1</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|3=<del style="font-weight: bold; text-decoration: none;">Merkatz</del>}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|3=<ins style="font-weight: bold; text-decoration: none;">Merksatz</ins>}}</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
</table>
Kilian Schoeller
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=79118&oldid=prev
Kilian Schoeller am 3. Dezember 2018 um 11:04 Uhr
2018-12-03T11:04:53Z
<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 3. Dezember 2018, 11:04 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l17">Zeile 17:</td>
<td colspan="2" class="diff-lineno">Zeile 17:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Frage|2=Eine lineare Funktion f hat die Steigung <math>m = 1,5</math> und verläuft durch den Punkt <math>A(2|0,5)</math>.<br><br> Wie würdest du vorgehen, um den Funktoinsterm der Funktion zu bestimmmen, <u>''ohne''</u> den Graphen zu zeichnen? <br>Dokumentiere deine Überlegungen im Schulheft.<br><br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{Box|1=Frage|2=Eine lineare Funktion f hat die Steigung <math>m = 1,5</math> und verläuft durch den Punkt <math>A(2|0,5)</math>.<br><br> Wie würdest du vorgehen, um den Funktoinsterm der Funktion zu bestimmmen, <u>''ohne''</u> den Graphen zu zeichnen? <br>Dokumentiere deine Überlegungen im Schulheft.<br><br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Du kommst nicht drauf? Oder bist dir nicht sicher? <br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Du kommst nicht drauf? Oder bist dir nicht sicher? <br></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Hilfe zur Selbsthilfe:'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Hilfe zur Selbsthilfe:'''</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>{{LearningApp|app=p211tz58c01|width=800px|height=500px}}</center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center>{{LearningApp|app=p211tz58c01|width=800px|height=500px}}</center></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|3=Arbeitsmethode}}</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">Löung </del>versteckt|1=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">Lösung </ins>versteckt|1=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*f ist linear, also gilt f(x) = m* x + t<br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*f ist linear, also gilt f(x) = m* x + t<br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*f(x) = 1,5* x +t (Steigung ist ja gegeben)<br></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*f(x) = 1,5* x +t (Steigung ist ja gegeben)<br></div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===4.2 Funktionsterm aus zwei gegebenen Punkten bestimmen===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===4.2 Funktionsterm aus zwei gegebenen Punkten bestimmen===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">Merke</del>|1=Bestimmung der Funktionsgleichung, wenn zwei Punkte bekannt sind|2=</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">Box</ins>|1=Bestimmung der Funktionsgleichung, wenn zwei Punkte bekannt sind|2=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Beispiel:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Beispiel:</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l58">Zeile 58:</td>
<td colspan="2" class="diff-lineno">Zeile 61:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f (4) = 5, also 0,5 * 4 + t = 5 und damit t = 3.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>f (4) = 5, also 0,5 * 4 + t = 5 und damit t = 3.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet: <math>f(x) = 0,5 x + 3</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Die Funktiongleichung lautet: <math>f(x) = 0,5 x + 3</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|3=Merksatz</ins>}}</div></td></tr>
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</table>
Kilian Schoeller
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=79117&oldid=prev
Kilian Schoeller am 3. Dezember 2018 um 11:00 Uhr
2018-12-03T11:00:13Z
<p></p>
<a href="https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=79117&oldid=72116">Änderungen zeigen</a>
Kilian Schoeller
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=72116&oldid=prev
Maria Eirich am 16. November 2018 um 21:57 Uhr
2018-11-16T21:57:41Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 16. November 2018, 21:57 Uhr</td>
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<td colspan="2" class="diff-lineno">Zeile 2:</td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><div style=" width: 80%; border: 2px solid #c6d745; background-color:#c6d745; padding:7px;font-size:1px; height:1px; border-bottom:1px solid #c6d745;"></div></del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><div style=" width: 80%; border: 2px solid #c6d745; background-color:#ffffff; align:center; padding:7px;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Station 4: Aufstellen des Funktionsterms ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Station 4: Aufstellen des Funktionsterms ==</div></td></tr>
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Maria Eirich
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=50331&oldid=prev
Matthias Scharwies: 1 Version importiert
2018-04-07T12:17:20Z
<p>1 Version importiert</p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td>
<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Version vom 7. April 2018, 12:17 Uhr</td>
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Matthias Scharwies
https://unterrichten.zum.de/index.php?title=Lineare_Funktionen/Station_4&diff=50330&oldid=prev
Main>Karl Kirst: Merksatz > Merke
2018-03-11T11:06:03Z
<p>Merksatz > Merke</p>
<p><b>Neue Seite</b></p><div>{{Lernpfad Lineare Funktionen}}<br />
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==Station 4: Aufstellen des Funktionsterms ==<br />
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|align = "left" width="200"|[[Datei:Refugees-1015294 1920.jpg|290px|Schlussetappe]]<br />
|align = "left" |'''Schlussetappe!''' In Station 3 hast du gelernt, wie die Funktionsgleichung linearer Funktionen aussieht und wie man den Funktionsterm am Graphen ablesen kann.<br />
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'''In dieser Station lernst du, wie man den Funktionsterm aufstellen kann, wenn nur wenige Angaben zur Verfügung stehen.'''<br />
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===4.1 Funktionsterm aus gegebenem Punkt und Steigung bestimmen===<br />
In diesem Abschnitt geht es darum, folgende Frage zu klären:<br><br><br />
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{{Frage|Eine lineare Funktion f hat die Steigung <math>m = 1,5</math> und verläuft durch den Punkt <math>A(2|0,5)</math>.<br><br> Wie würdest du vorgehen, um den Funktoinsterm der Funktion zu bestimmmen, <u>''ohne''</u> den Graphen zu zeichnen? <br>Dokumentiere deine Überlegungen im Schulheft.<br><br><br />
Du kommst nicht drauf? Oder bist dir nicht sicher? <br><br />
'''Hilfe zur Selbsthilfe:'''<br> <iframe src="//LearningApps.org/watch?v=p211tz58c01" style="border:0px;width:30%;height:90px" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe><br />
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*f ist linear, also gilt f(x) = m* x + t<br><br />
*f(x) = 1,5* x +t (Steigung ist ja gegeben)<br><br />
''Wir müssen also im Endeffekt nur noch den y-Achsenabschnitt t bestimmen, oder?''<br><br />
*A(2{{!}}0,5) liegt auf f, also f(2) = 0,5 und sowieso f(2) = 1,5 * 2 + t<br />
*Also: 1,5 * 2 + t = 0,5 oder kurz 3+t=0,5<br />
*Damit: t=0,5-3 = -2,5<br><br><br />
Die Funktionsgleichung lautet: <math>f(x)=1,5\cdot x -2,5</math></div><br />
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{{Merke|1=Allgemein gilt: Um die Funktionsgleichung bzw. den Funktionsterm einer linearen Funktion zu bestimmen, muss man nur die <span style = "color:blue">'''Steigung m'''</span> und den <span style = "color:red">'''y-Achsenabschnitt t'''</span> bestimmen. <br><br />
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{{Merke|1=Bestimmung der Funktionsgleichung, wenn <u>ein Punkt und die Steigung bekannt</u> sind.<br><br><br />
<u>Beispiel:</u> lineare Funktion ''f'' hat die Steigung <span style = "color:blue">'''m = 3'''</span> und verläuft durch den Punkt <span style = "color:darkgreen">A(1 {{!}} 4)</span>.<br><br />
f ist linear, also f (x) = mx + t.<br><br><br />
'''Es muss nur noch t bestimmt werden!'''<br><br><br />
f (x) = <span style = "color:blue">'''3'''</span>x + t<br><br />
f (<span style = "color:darkgreen">1</span>) = <span style = "color:darkgreen">4</span> also <span style = "color:blue">3</span>*<span style = "color:darkgreen">1</span> + t = <span style = "color:darkgreen">4</span> und damit <span style = "color:red">'''t = 1'''</span><br><br><br />
Die Funktiongleichung lautet: <math>f(x) = \color{blue}{3} x + \color{red}{1}</math><br />
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|<div style="font: 10pt Verdana; font-weight:bold; padding:5px; border-bottom:1px solid #AAAAAA;">[[Bild:Hand.gif|30px]] <br />
&nbsp; Übung 12: Bestimme die Funktionsgleichung!<br />
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===4.2 Funktionsterm aus zwei gegebenen Punkten bestimmen===<br />
{{Merke|1=Bestimmung der Funktionsgleichung, wenn <u>zwei Punkte bekannt</u> sind.<br><br><br />
<u>Beispiel:</u> lineare Funktion ''f'' verläuft durch die Punkte <span style = "color:darkgreen">A(4 {{!}} 5)</span> und <span style = "color:darkblue">A(-4 {{!}} 1)</span>.<br><br><br />
'''Zunächst muss die Steigung m bestimmt werden!'''<br><br><br />
<math>m=\frac{\Delta y}{\Delta x}=\frac{y_B-y_A}{x_B-x_A}=\frac{5-1}{4-(-4)}=\frac{4}{8}=0,5</math><br><br><br />
'''Nun muss wie oben noch t bestimmt werden!''' Nehme entweder Punkt A oder B zu Hilfe.<br><br><br />
f (x) = <span style = "color:blue">'''0,5'''</span>x + t<br><br />
f (<span style = "color:darkgreen">'''4'''</span>) = <span style = "color:darkgreen">'''5'''</span> also <span style = "color:blue">'''0,5'''</span>*<span style = "color:darkgreen">'''4'''</span> + '''t''' = <span style = "color:darkgreen">'''5'''</span> und damit <span style = "color:red">'''t = 3'''</span><br><br><br />
Die Funktiongleichung lautet: <math>f(x) = \color{blue}{0,5} x + \color{red}{3}</math><br />
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{|<br />
|Nimm dir bitte kurz Zeit, und gib eine Rückmeldung zu dieser Station. <br><br />
<iframe src="//LearningApps.org/watch?v=pbvaenrrj01" style="border:0px;width:60%;height:90px" webkitallowfullscreen="true" mozallowfullscreen="true"></iframe><br />
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'''Alle Aufgaben erledigt? Dann kann's weitergehen!'''<br />
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|align = "left"|[[/Übung|'''Hier geht es weiter zur letzten Übung...''']]'''...'''<br />
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{{Lernpfad Lineare Funktionen}}</div>
Main>Karl Kirst