Function Transformations (2)
2013-08-06 03:26
This example explores how changes in function expressions affect function graphs, demonstrating geometric transformations such as translations and reflections. Through dynamic interaction, users can observe the correspondence between functions f(x) and g(x) as parameters change, understanding the algebraic and geometric significance of function transformations. Supports multilingual switching and
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<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Point">
<input a0="f"/>
<output a0="P_0"/>
</command>
<element type="point" label="P_0">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="0.03412087473291703" y="-0.34132497913844473" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="ClosestPoint">
<input a0="list1" a1="P_0"/>
<output a0="P_1"/>
</command>
<element type="point" label="P_1">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="0" y="-0.3333333333333333" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="Q_0"/>
</command>
<element type="point" label="Q_0">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="-7.999999999999897" y="-32.999999999998316" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="ClosestPoint">
<input a0="list2" a1="Q_0"/>
<output a0="Q_1"/>
</command>
<element type="point" label="Q_1">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="-4" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="d" exp="AxisStepX[] / 10" />
<element type="numeric" label="d">
<value val="0.1"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="DynamicCoordinates">
<input a0="P_0" a1="If[Distance[P_0, P_1] < d, x(P_1), x(P_0)]" a2="If[Distance[P_0, P_1] < d, y(P_1), y(P_0)]"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="true" label="true"/>
<condition showObject="showFreePoints"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="15" y="39"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="0" y="-0.3333333333333333" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="DynamicCoordinates">
<input a0="Q_0" a1="If[Distance[Q_0, Q_1] < d, x(Q_1), x(Q_0)]" a2="If[Distance[Q_0, Q_1] < d, y(Q_1), y(Q_0)]"/>
<output a0="P'"/>
</command>
<element type="point" label="P'">
<show object="true" label="true"/>
<condition showObject="showGraph ∧ showFreePoints ∧ (¬equal)"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelOffset x="-1" y="34"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="1" playing="false"/>
<isShape val="false"/>
<coords x="-7.999999999999897" y="-32.999999999998316" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>