构造一次函数图像
2017-11-20 14:39
本范例演示了如何在GeoGebra中构造和探索一次函数（线性函数）。通过定义点、线段和多边形等几何对象，结合坐标和向量，直观地展示线性函数的图像特征及其几何变换。适合用于理解函数图像、坐标系以及几何作图的基本概念，帮助学生掌握线性函数的代数与几何性质。
所属专题
初中函数
GeoGebra 画板及绘图内容加载中，请稍等……
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<element type="boolean" label="checker">
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<labelMode val="0"/>
<checkbox fixed="true"/>
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<expression label="filled" exp="(((((x1 * x2) * x3) * y1) * y2) * y3) > 0" />
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<show object="false" label="true"/>
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<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
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<expression label="text10" exp=""x""/>
<element type="text" label="text10">
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<show object="true" label="true" ev="8"/>
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<font serif="false" sizeM="4" size="36" style="1"/>
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<expression label="text11" exp=""y""/>
<element type="text" label="text11">
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<command name="Sequence">
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<element type="list" label="anchors">
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<show object="true" label="false" ev="4"/>
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<expression label ="gridSpacer" exp="0.7"/>
<element type="numeric" label="gridSpacer">
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<symbolic val="true" />
<show object="false" label="false"/>
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<animation step="1" speed="1" type="0" playing="false"/>
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<command name="Point">
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<element type="point" label="fakeOrigin">
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<command name="Sequence">
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<output a0="verLines"/>
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<element type="list" label="verLines">
<show object="true" label="false" ev="4"/>
<objColor r="96" g="96" b="96" alpha="0"/>
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<command name="Sequence">
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<element type="list" label="horLines">
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<command name="Vector">
<input a0="fakeOrigin" a1="fakeOrigin + ((11 * gridSpacer), 0)"/>
<output a0="xaxis"/>
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<element type="vector" label="xaxis">
<show object="true" label="false" ev="4"/>
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<coordStyle style="cartesian"/>
<startPoint exp="fakeOrigin"/>
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<command name="Vector">
<input a0="fakeOrigin" a1="fakeOrigin + (0, (11 * gridSpacer))"/>
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<element type="vector" label="yaxis">
<show object="true" label="false" ev="4"/>
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<element type="point" label="point1anchor">
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<element type="point" label="point3anchor">
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<animation step="1" speed="5" type="3" playing="false"/>
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<element type="numeric" label="colorChangeTimer">
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<show object="false" label="false"/>
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<ggbscript onUpdate="StartAnimation[timer1,colorChangeTimer==1]"/>
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<command name="Join">
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<animation step="1" speed="5" type="3" playing="false"/>
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<expression label="poly1outline" exp="poly1" />
<element type="polygon" label="poly1outline">
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<expression label="poly2outline" exp="poly2" />
<element type="polygon" label="poly2outline">
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<expression label="poly4outline" exp="poly4" />
<element type="polygon" label="poly4outline">
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<expression label="poly5outline" exp="poly5" />
<element type="polygon" label="poly5outline">
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<expression label="poly7outline" exp="poly7" />
<element type="polygon" label="poly7outline">
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<element type="polygon" label="poly8outline">
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<symbolic val="true" />
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<element type="boolean" label="firstCheck">
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<element type="point" label="old1">
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<condition showObject="checkedTimer > 0 ∧ checkedTimer < 1"/>
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<element type="point" label="old2">
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<condition showObject="checkedTimer > 0 ∧ checkedTimer < 1"/>
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<element type="point" label="old3">
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<condition showObject="checkedTimer > 0 ∧ checkedTimer < 1"/>
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<element type="numeric" label="checkedTimer">
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<symbolic val="true" />
<show object="false" label="false"/>
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<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="5" type="3" playing="false"/>
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<element type="button" label="button3">
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<condition showObject="filled ∧ doubleChecker ≟ 6 ∧ timer3 ≟ Length[path3] ∧ (moved1 ∨ moved2 ∨ moved3)"/>
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<layer val="4"/>
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<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[firstCheck,true] SetValue[checker,true] SetValue[old1,point1anchor] SetValue[old2,point2anchor] SetValue[old3,point3anchor] If(IsInRegion[A,poly1],SetValue[A,Centroid[poly1]]) If(IsInRegion[A,poly2],SetValue[A,Centroid[poly2]]) If(IsInRegion[A,poly4],SetValue[A,Centroid[poly4]]) If(IsInRegion[A,poly5],SetValue[A,Centroid[poly5]]) If(IsInRegion[A,poly7],SetValue[A,Centroid[poly7]]) If(IsInRegion[A,poly8],SetValue[A,Centroid[poly8]]) If(IsInRegion[B,poly1],SetValue[B,Centroid[poly1]]) If(IsInRegion[B,poly2],SetValue[B,Centroid[poly2]]) If(IsInRegion[B,poly4],SetValue[B,Centroid[poly4]]) If(IsInRegion[B,poly5],SetValue[B,Centroid[poly5]]) If(IsInRegion[B,poly7],SetValue[B,Centroid[poly7]]) If(IsInRegion[B,poly8],SetValue[B,Centroid[poly8]]) If(IsInRegion[C,poly1],SetValue[C,Centroid[poly1]]) If(IsInRegion[C,poly2],SetValue[C,Centroid[poly2]]) If(IsInRegion[C,poly4],SetValue[C,Centroid[poly4]]) If(IsInRegion[C,poly5],SetValue[C,Centroid[poly5]]) If(IsInRegion[C,poly7],SetValue[C,Centroid[poly7]]) If(IsInRegion[C,poly8],SetValue[C,Centroid[poly8]]) If(IsInRegion[D,poly1],SetValue[D,Centroid[poly1]]) If(IsInRegion[D,poly2],SetValue[D,Centroid[poly2]]) If(IsInRegion[D,poly4],SetValue[D,Centroid[poly4]]) If(IsInRegion[D,poly5],SetValue[D,Centroid[poly5]]) If(IsInRegion[D,poly7],SetValue[D,Centroid[poly7]]) If(IsInRegion[D,poly8],SetValue[D,Centroid[poly8]]) If(IsInRegion[E,poly1],SetValue[E,Centroid[poly1]]) If(IsInRegion[E,poly2],SetValue[E,Centroid[poly2]]) If(IsInRegion[E,poly4],SetValue[E,Centroid[poly4]]) If(IsInRegion[E,poly5],SetValue[E,Centroid[poly5]]) If(IsInRegion[E,poly7],SetValue[E,Centroid[poly7]]) If(IsInRegion[E,poly8],SetValue[E,Centroid[poly8]]) If(IsInRegion[F,poly1],SetValue[F,Centroid[poly1]]) If(IsInRegion[F,poly2],SetValue[F,Centroid[poly2]]) If(IsInRegion[F,poly4],SetValue[F,Centroid[poly4]]) If(IsInRegion[F,poly5],SetValue[F,Centroid[poly5]]) If(IsInRegion[F,poly7],SetValue[F,Centroid[poly7]]) If(IsInRegion[F,poly8],SetValue[F,Centroid[poly8]]) If(IsInRegion[G,poly1],SetValue[G,Centroid[poly1]]) If(IsInRegion[G,poly2],SetValue[G,Centroid[poly2]]) If(IsInRegion[G,poly4],SetValue[G,Centroid[poly4]]) If(IsInRegion[G,poly5],SetValue[G,Centroid[poly5]]) If(IsInRegion[G,poly7],SetValue[G,Centroid[poly7]]) If(IsInRegion[G,poly8],SetValue[G,Centroid[poly8]]) If(IsInRegion[H,poly1],SetValue[H,Centroid[poly1]]) If(IsInRegion[H,poly2],SetValue[H,Centroid[poly2]]) If(IsInRegion[H,poly4],SetValue[H,Centroid[poly4]]) If(IsInRegion[H,poly5],SetValue[H,Centroid[poly5]]) If(IsInRegion[H,poly7],SetValue[H,Centroid[poly7]]) If(IsInRegion[H,poly8],SetValue[H,Centroid[poly8]]) If(IsInRegion[I,poly1],SetValue[I,Centroid[poly1]]) If(IsInRegion[I,poly2],SetValue[I,Centroid[poly2]]) If(IsInRegion[I,poly4],SetValue[I,Centroid[poly4]]) If(IsInRegion[I,poly5],SetValue[I,Centroid[poly5]]) If(IsInRegion[I,poly7],SetValue[I,Centroid[poly7]]) If(IsInRegion[I,poly8],SetValue[I,Centroid[poly8]]) SetValue[point1anchor, fakeOrigin+gridSpacer*(x1,y1)] SetValue[point2anchor, fakeOrigin+gridSpacer*(x2,y2)] SetValue[point3anchor, fakeOrigin+gridSpacer*(x3,y3)] SetValue[checker,true] SetValue[checkedTimer,0] StartAnimation[checkedTimer] "/>
<font serif="false" sizeM="2" size="12" style="0"/>
<caption val="Check"/>
</element>
<expression label="newMover1" exp="(old1 * (1 - checkedTimer)) + (point1anchor * checkedTimer)" type="point" />
<element type="point" label="newMover1">
<show object="false" label="false" ev="4"/>
<condition showObject="firstCheck"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="11.5" y="2.1999999999999993" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<expression label="newMover2" exp="(old2 * (1 - checkedTimer)) + (point2anchor * checkedTimer)" type="point" />
<element type="point" label="newMover2">
<show object="false" label="false" ev="4"/>
<condition showObject="firstCheck"/>
<objColor r="255" g="215" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="12.899999999999999" y="3.5999999999999996" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<expression label="moved1" exp="point1anchor ≠ fakeOrigin + (gridSpacer * (x1, y1))" />
<element type="boolean" label="moved1">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="moved2" exp="point2anchor ≠ fakeOrigin + (gridSpacer * (x2, y2))" />
<element type="boolean" label="moved2">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="moved3" exp="point3anchor ≠ fakeOrigin + (gridSpacer * (x3, y3))" />
<element type="boolean" label="moved3">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text13" exp=""This graph is not entirely accurate!""/>
<element type="text" label="text13">
<show object="true" label="true" ev="40"/>
<condition showObject="(moved1 ∨ moved2 ∨ moved3) ∧ timer3 ≟ Length[path3]"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="4" size="36" style="1"/>
<startPoint x="8.309299895506786" y="2.74101985370951" z="1"/>
</element>
<command name="Join">
<input a0="{Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point3anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point3anchor), y(fakeOrigin)) * (1 - i / 300)) + (point3anchor * i / 300), i, 0, 300]}"/>
<output a0="path3"/>
</command>
<element type="list" label="path3">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Element" type="point">
<input a0="path3" a1="timer3"/>
<output a0="mover3"/>
</command>
<element type="point" label="mover3">
<show object="true" label="false" ev="4"/>
<condition showObject="timer2 ≟ Length[path2] ∧ (¬firstCheck)"/>
<objColor r="220" g="20" b="60" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="8" y="-2" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<expression label="newMover3" exp="(old3 * (1 - checkedTimer)) + (point3anchor * checkedTimer)" type="point" />
<element type="point" label="newMover3">
<show object="true" label="false" ev="4"/>
<condition showObject="firstCheck"/>
<objColor r="220" g="20" b="60" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="10.8" y="4.3" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="Join">
<input a0="{Sequence[(fakeOrigin * (1 - i / 300)) + ((x(point1anchor), y(fakeOrigin)) * i / 300), i, 0, 300], Sequence[((x(point1anchor), y(fakeOrigin)) * (1 - i / 300)) + (point1anchor * i / 300), i, 0, 300]}"/>
<output a0="path1"/>
</command>
<element type="list" label="path1">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Element" type="point">
<input a0="path1" a1="timer1"/>
<output a0="mover1"/>
</command>
<element type="point" label="mover1">
<show object="true" label="false" ev="4"/>
<condition showObject="timer1 > 1 ∧ (¬firstCheck)"/>
<objColor r="0" g="255" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="8" y="-2" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="¬firstCheck" a1="Line[mover1, mover2]" a2="Line[newMover1, newMover2]"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="{x(fakeOrigin) - gridSpacer, g(x(fakeOrigin) - gridSpacer)}"/>
<output a0="leftBound"/>
</command>
<element type="point" label="leftBound">
<show object="false" label="false" ev="4"/>
<objColor r="220" g="20" b="60" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="7.3" y="NaN" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="{x(fakeOrigin) + (11 * gridSpacer), g(x(fakeOrigin) + (11 * gridSpacer))}"/>
<output a0="rightBound"/>
</command>
<element type="point" label="rightBound">
<show object="false" label="false" ev="4"/>
<objColor r="220" g="20" b="60" alpha="0"/>
<layer val="4"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="15.7" y="NaN" z="1"/>
<pointSize val="7"/>
<pointStyle val="0"/>
</element>
<command name="If">
<input a0="¬firstCheck" a1="Vector[mover1, leftBound]" a2="Vector[newMover1, leftBound]"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="4"/>
<condition showObject="line ∧ ready"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="12" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="newMover1"/>
</element>
<command name="If">
<input a0="¬firstCheck" a1="Vector[mover1, rightBound]" a2="Vector[newMover1, rightBound]"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="line ∧ ready"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isShape val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="12" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="newMover1"/>
</element>
<command name="If">
<input a0="¬firstCheck" a1="timer3 ≟ Length[path3]" a2="checkedTimer ≟ 1"/>
<output a0="ready"/>
</command>
<element type="boolean" label="ready">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
</construction>
</geogebra>