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      <text>2.2.1.1The Graph of a Function</text>
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    <questiontext format="html">
      <text><![CDATA[<h3 style="text-align: left;"><span style="color: inherit; font-family: inherit;">The Graph of a Function</span><br></h3>
<p>Consider the function \(f(x)=2x\). The output is obtained by multiplying the input by \(2\). We can choose several values for the input to this function and calculate the corresponding outputs. We have done this for integer values of <span class="math inline">\(x\)</span> between \(-2\) and \(2\) and the results are shown in the table below.</p>

<table class="HELM_table">
<thead>
<tr>
<th>input, \(x:\)</th>
<th>\(-2\)</td>
<th>\(-1\)</td>
<th>\(0\)</td>
<th>\(1\)</td>
<th>\(2\)</td>
</tr></thead><tbody>
<tr>
<td><b>output, \(\:f(x):\)</b></td>
<td>\(-4\)</td>
<td>\(-2\)</td>
<td>\(0\)</td>
<td>\(2\)</td>
<td>\(4\)</td>
</tr>
</tbody>
</table>

<p>To construct the graph of this function we first draw a pair of <span><strong>axes</strong></span> &ndash; a vertical axis and a horizontal axis. These are drawn at right-angles to each other and intersect as shown in the figure below.</p><br>
<figure class="HELM_figure">
<img src="@@PLUGINFILE@@/2.2-fig1-linear_function.svg" alt="" width="373" height="179" class="img-responsive atto_image_button_text-bottom">
<figcaption>The two axes intersect at the origin</figcaption>
</figure>
<p>Each pair of input and output values can be represented on a graph by a single point. The input values are measured along the horizontal axis and the output values are measured along the vertical axis. The horizontal axis is often called the \(x\) axis. The vertical axis is commonly referred to as the \(y\) axis so that we often write the function as \[
y=f(x)=2x \] or simply \[y=2x.\] </p>
<p>Each pair of \(x\) and \(y\) values in the table is plotted as a single point, shown as \(\bullet\) in the figure above. A general point is often labelled as \((x,y)\). The values \(x\) and \(y\) are said to be the <span><strong>coordinates</strong></span> of the point. The points are then joined with a smooth curve to produce the required graph as shown in the figure above. Note that in this case the graph is a straight line. The graph can then be used to find function values other than those given in the table. For example, directly from the graph we can see that when \(x=1.5\), the value of \(y\) is \(3\).</p>]]></text>
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<file name="fig7.svg" path="/" encoding="base64">[encoded data, 37120 characters]</file>
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