Plotting Inverse Proportion Function Graphs Using Point-Plotting Method
2020-04-19 13:48
This applet demonstrates plotting an inverse proportion function graph using the point-plotting method. It visually illustrates the hyperbolic characteristics and quadrant distribution of functions like y=k/x through tabulating, plotting, and connecting points. Ideal for students to understand the graphical properties and drawing techniques of inverse proportion functions.
In collections
初中函数
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="d" id="d8f2e20c-3a98-4055-9943-774bfe0bc0c6" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1382" height="744" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2503617945007236" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1" size="380" window="333,89,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1355" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="346" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="14"/>
<consProtColumns col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1355" height="568"/>
<coordSystem xZero="279.9773264463915" yZero="285.22249546027103" scale="20.390942419022778" yscale="20.390942419022778"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="2" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="k">
<value val="12.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-12" max="12" absoluteScreenLocation="true" width="200.0" x="760.0" y="335.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="3" playing="false"/>
</element>
<element type="numeric" label="l">
<value val="12.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="Length[l1]" absoluteScreenLocation="true" width="200.0" x="30.0" y="130.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="3" playing="false"/>
</element>
<command name="Sort">
<input a0="Flatten[{DivisorsList[12], (-DivisorsList[12])}]"/>
<output a0="l1"/>
</command>
<element type="list" label="l1">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="If[k / Element[l1, t] < 0, "-", ""] + (FractionText[abs(k / Element[l1, t])])" a1="t" a2="1" a3="l"/>
<output a0="l3'"/>
</command>
<element type="list" label="l3'">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="numeric" label="m">
<value val="12.0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="Length[l1]" absoluteScreenLocation="true" width="200.0" x="30.0" y="170.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="3" playing="false"/>
</element>
<element type="numeric" label="n">
<value val="12.1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="Min[l1] - 0.5" max="Max[l1] + 0.1" absoluteScreenLocation="true" width="200.0" x="30.0" y="210.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation speed="3" type="3" playing="false"/>
</element>
<command name="Flatten">
<input a0="{"x", "...", l1, "..."}"/>
<output a0="l2"/>
</command>
<element type="list" label="l2">
<objColor r="0" g="100" b="0" alpha="0.0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<expression label="l3" exp="k / Take[l1, 1, l]" />
<element type="list" label="l3">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="Flatten">
<input a0="{"y", "...", l3', If[l ≟ Length[l1], "..."]}"/>
<output a0="l4"/>
</command>
<element type="list" label="l4">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="755" y="245"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="StartAnimation[l]"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<caption val="列表"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="850" y="244"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="StartAnimation[m]"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<caption val="描点"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="947" y="244"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="StartAnimation[n]"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<caption val="连线"/>
</element>
<element type="button" label="button4">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="1043" y="243"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[l,0]
SetValue[m,0]
SetValue[n,Min(l1) - 0.5]"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<caption val="复位"/>
</element>
<command name="LaTeX">
<input a0=""y=\frac{k}{x}\ (k≠0)""/>
<output a0="text1"/>
</command>
<element type="text" label="text1">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="14" style="0"/>
<absoluteScreenLocation x="741" y="-3"/>
</element>
<command name="If">
<input a0="k ≟ 0" a1=""错误"" a2="LaTeX["y=\frac{" + k + "}{x}"]"/>
<output a0="text2"/>
</command>
<element type="text" label="text2">
<show object="true" label="false" ev="8"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2.0" size="14" style="0"/>
<absoluteScreenLocation x="741" y="79"/>
</element>
<command name="TableText">
<input a0="l2" a1="l4" a2=""c_|""/>
<output a0="text3"/>
</command>
<element type="text" label="text3">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.2" size="3" style="0"/>
<absoluteScreenLocation x="654" y="155"/>
</element>
<expression label="f" exp="f(x) = If[Element[l1, 1] - 0.5 ≤ x ≤ If[n < -1, n, -1 + 0.1], k / x]" />
<element type="function" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="g" exp="g(x) = If[1 - 0.1 ≤ x ≤ n + 0.5, k / x]" />
<element type="function" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
</element>
<command name="Sequence">
<input a0="(Element[l1, t], Element[l3, t])" a1="t" a2="1" a3="m"/>
<output a0="l5"/>
</command>
<element type="list" label="l5">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="33.44733458309152" y="-11.72959540686062" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="41.198093947575124" y="-11.72959540686062" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="124d9c580701baaed8c3a55143691816/反比例.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="A"/>
<startPoint number="1" exp="B"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="41.78436955217693" y="-13.004671343308978" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="50.301425419751915" y="-13.004671343308978" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic2">
<file name="a94857e5933a1326ec9a95938feb52d3/公众号 二维码.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="C"/>
<startPoint number="1" exp="D"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text4" exp=""制作教程：""/>
<element type="text" label="text4">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="2.0" size="14" style="0"/>
<startPoint x="25.64975481788811" y="-7.835709662476022" z="1.0"/>
</element>
</construction>
</geogebra>