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      <text>2.3.2 (When is a relation a function?)</text>
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      <text><![CDATA[<h3>When is a relation a function?</h3>
<p>Clearly it is important to decide if a given equation is a function. Fortunately there are a couple of ways that we can do this. Firstly we can use the definition of a function to see if any value of \(x\) give at most one value of \(y\). For example \[ y = 13x-10 \qquad \mbox{is a function because for every value of } x \mbox{ there is one value of } y \] \[ x = y^2 \qquad \mbox{is not a function since if } x = 9 \mbox{ then } y = \pm 3. \] It is also possible to determine when we have a function by reading off the graphs of the given equation This is sometimes called the <em>vertical line test</em>. The idea is that if we draw a vertical line at any point on the graph of a relation if the vertical line intersects the graph once then the relation is a function, if the line intersects the graph more than once then it is not a function.</p>
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<p><img style="display: block; margin-left: auto; margin-right: auto;" src="@@PLUGINFILE@@/Vertical%20line%20test.png" alt="Vertical line test for a function and not a function" width="789" height="366" /></p>]]></text>
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