範例：繪製不等式與分段函數

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範例：繪製不等式與分段函數

使用繪圖展示不等式及分段函數。

不等式

1. 在空圖中，於 y 軸運算式中輸入不等式，於 x 軸運算式中輸入對應的自變數。

按一下以複製此運算式

<region id="ID0ER6DHB" top="216" left="24" width="411.2" 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 num-of-points="500">
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">線條</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 />
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">r</id>
              </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 />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <greaterThan />
                  <apply>
                    <scale />
                    <real>2</real>
                    <id>r</id>
                  </apply>
                  <real>5</real>
                </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>

因為不等式是布林運算式，所以 PTC Mathcad 會繪製為「真」的 r 值 (>2.5) 及為「假」的 r 值 (<2.5)。為「真」時不等式等於 1，為「假」時等於 0。

2. 使用 AND 運算子將第二個不等式加入第一個。

按一下以複製此運算式

<region id="ID0EHCEHB" top="624" left="24" width="440.8" 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 num-of-points="500">
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">線條</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 />
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">r</id>
              </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 />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <and />
                  <parens>
                    <apply>
                      <greaterThan />
                      <apply>
                        <scale />
                        <real>2</real>
                        <id>r</id>
                      </apply>
                      <real>5</real>
                    </apply>
                  </parens>
                  <parens>
                    <apply>
                      <lessThan />
                      <id>r</id>
                      <apply>
                        <div />
                        <real>20</real>
                        <real>3</real>
                      </apply>
                    </apply>
                  </parens>
                </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>

分段函數

在整個值域中未保持均等的函數，稱為分段函數。若要繪製分段函數，必須使用內建的條件式函數 if。

1. 定義函數並繪製在特定的區域上。

按一下以複製此運算式

<region id="ID0EXFEHB" top="1032" left="0" width="341" height="257.8" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">線條</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="ticknumberlock" positionticmark="1" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">x</id>
              </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>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">-1</real>
            </secondTickValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">2</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="ticknumberlock" positionticmark="2" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>f</id>
                  <id>x</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>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </secondTickValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">3</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

2. 定義並繪製等於 f(x) 的分段函數 (僅當 f(x) > 0 時)。

按一下以複製此運算式

<region id="ID0E4HEHB" top="1368" left="0" width="370" height="278" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false">
    <xyPlot>
      <title class="- topic/title " wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">線條</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="ticknumberlock" positionticmark="0" />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">x</id>
              </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>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">-1</real>
            </secondTickValue>
            <endValue>
              <placeholder xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="ticknumberlock" positionticmark="2" />
          <axisGrid>
            <gridFrequency>4</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>g</id>
                  <id>x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </secondTickValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">3</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

3. 使用 AND 運算子定義 x 的值域，在其上繪製此類 f(x)。至於其他的 x 值，請繪製 f 的負函數。

<region id="ID0E4JEHB" top="1800" left="24" width="217.893333333333" height="21.2" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math>
    <define xmlns="http://schemas.mathsoft.com/math50">
      <function>
        <id label="Variable">h</id>
        <boundVars>
          <id label="Variable">x</id>
        </boundVars>
      </function>
      <apply>
        <id label="Keyword">if</id>
        <sequence>
          <apply>
            <and />
            <parens>
              <apply>
                <lessThan />
                <real>-1</real>
                <id>x</id>
              </apply>
            </parens>
            <parens>
              <apply>
                <lessThan />
                <id>x</id>
                <real>1</real>
              </apply>
            </parens>
          </apply>
          <apply>
            <id>f</id>
            <id>x</id>
          </apply>
          <apply>
            <neg />
            <apply>
              <id>f</id>
              <id>x</id>
            </apply>
          </apply>
        </sequence>
      </apply>
    </define>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" />
    </resultFormat>
  </math>
</region>

按一下以複製此運算式

<region id="ID0ELKEHB" top="1824" left="24" width="312" height="277" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false">
    <xyPlot>
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      <legend />
      <traces>
        <trace>
          <traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">線條</traceStyle>
        </trace>
      </traces>
      <axes>
        <xAxis legend-position="PlotBoundaryBottom" rank="1">
          <axisLine position="ticknumberlock" positionticmark="4" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <id xmlns="http://schemas.mathsoft.com/math50">x</id>
              </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>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">-1</real>
            </secondTickValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">2</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis legend-position="PlotBoundaryLeft" rank="1">
          <axisLine position="ticknumberlock" positionticmark="2" />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <markers />
          <numberFormat />
          <plotEquations>
            <plotEquation>
              <math>
                <apply xmlns="http://schemas.mathsoft.com/math50">
                  <id>h</id>
                  <id>x</id>
                </apply>
              </math>
              <math>
                <placeholder xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true">
            <startValue>
              <real xmlns="http://schemas.mathsoft.com/math50">-2</real>
            </startValue>
            <secondTickValue>
              <real xmlns="http://schemas.mathsoft.com/math50">-1.5</real>
            </secondTickValue>
            <endValue>
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

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