Example: Using Range Variables in Plots

Plots > XY Plots > Plotting Functions > Example: Using Range Variables in Plots

Use range variables when plotting functions to control the number of plotted points and the range over which functions are plotted.

1. Define a range variable.

2. Use the range variable as the independent variable in a parametric plot. Add crosses from the Symbols list to mark the location of the plotted points.

<region id="ID0E6SDHB" top="216" left="24" width="448" height="312" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="origin" positionticmark="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>cos</id>
                  <id>i</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="origin" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>sin</id>
                  <id>i</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

3. To increase the number of plotted points, repeat steps 1 and 2 with a range variable that has a step size of 0.1.

<region id="ID0E5UDHB" top="600" left="24" width="452" height="272" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="origin" positionticmark="0" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>cos</id>
                  <id>j</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="origin" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>sin</id>
                  <id>j</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

You can view the points plotted in the first two plots:

Range Variable	Y-axis expression	X-axis expression
<region id="ID0EVXDHB" top="936" left="24" width="48.8116666666667" height="64.331" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <id>i</id> <result> <matrix rows="4" cols="1"> <real>0</real> <real>1</real> <real>2</real> <real>3</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0EDYDHB" top="936" left="120" width="96.7216666666667" height="64.331" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id>sin</id> <id>i</id> </apply> <result> <matrix rows="4" cols="1"> <real>0</real> <real>0.841</real> <real>0.909</real> <real>0.141</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ERYDHB" top="936" left="288" width="105.015" height="64.331" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id>cos</id> <id>i</id> </apply> <result> <matrix rows="4" cols="1"> <real>1</real> <real>0.54</real> <real>-0.416</real> <real>-0.99</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>
<region id="ID0EDZDHB" top="1080" left="24" width="69.465" height="200.159" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <id>j</id> <result> <matrix rows="12" cols="1"> <real>0</real> <real>0.1</real> <real>0.2</real> <real>0.3</real> <real>0.4</real> <real>0.5</real> <real>0.6</real> <real>0.7</real> <real>0.8</real> <real>0.9</real> <real>1</real> <real>1.1</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0ERZDHB" top="1080" left="120" width="108.115" height="200.159" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id>sin</id> <id>j</id> </apply> <result> <matrix rows="12" cols="1"> <real>0</real> <real>0.1</real> <real>0.199</real> <real>0.296</real> <real>0.389</real> <real>0.479</real> <real>0.565</real> <real>0.644</real> <real>0.717</real> <real>0.783</real> <real>0.841</real> <real>0.891</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>	<region id="ID0E6ZDHB" top="1080" left="288" width="108.345" height="200.159" xmlns="http://schemas.mathsoft.com/worksheet50"> <math> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id>cos</id> <id>j</id> </apply> <result> <matrix rows="12" cols="1"> <real>1</real> <real>0.995</real> <real>0.98</real> <real>0.955</real> <real>0.921</real> <real>0.878</real> <real>0.825</real> <real>0.765</real> <real>0.697</real> <real>0.622</real> <real>0.54</real> <real>0.454</real> </matrix> </result> </eval> <resultFormat> <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" /> <matrix size="12,12" offset="0,0" /> </resultFormat> </math> </region>

4. To increase the range of the plotted points, repeat steps 1 and 2 with a range variable that has an end limit of 2 π.

<region id="ID0EE3DHB" top="1344" left="24" width="369" height="312" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="true">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="Solid">lines</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="origin" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>cos</id>
                  <id>k</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="origin" positionticmark="5" />
          <axisGrid>
            <gridFrequency>11</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat>
            <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
          </numberFormat>
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>sin</id>
                  <id>k</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </startValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>