\( {a_{b}}^{c}+\sqrt[b]{a}= a_{b}^{c} \)\(  \)

<h2>Functions of the form \(y=x\)</h2>
<p>Functions of the form \(y=mx+c\) are called straight line functions. In the equation, \(y=mx+c\), \(m\) and \(c\) are constants and have different effects on the graph of the function.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<h3>Question</h3>
<div>\(y=f(x)=x\)

<p>Complete the following table for \(f(x)=x\) and plot the points on a set of axes.</p>
<table>
<tbody>
<tr>
<td>
<p>\(x\)</p>
</td>
<td>
<p>\(-\text{2}\)</p>
</td>
<td>
<p>\(-\text{1}\)</p>
</td>
<td>
<p>\(\text{0}\)</p>
</td>
<td>
<p>\(\text{1}\)</p>
</td>
<td>
<p>\(\text{2}\)</p>
</td>
</tr>
<tr>
<td>
<p>\(f(x)\)</p>
</td>
<td>
<p>\(-\text{2}\)</p>
</td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</tbody>
</table>
<ol>
<li>
<p>Join the points with a straight line.</p>
</li>
<li>
<p>Determine the domain and range.</p>
</li>
<li>
<p>About which line is \(f\) symmetrical?</p>
</li>
<li>
<p>Using the graph, determine the value of \(x\) for which \(f(x)=4\). Confirm your answer graphically.</p>
</li>
<li>
<p>Where does the graph cut the axes?</p>
</li>
</ol>
</div>
<div>
<h3>Substitute values into the equation</h3>
<table>
<tbody>
<tr>
<td>
<p>\(x\)</p>
</td>
<td>
<p>\(-\text{2}\)</p>
</td>
<td>
<p>\(-\text{1}\)</p>
</td>
<td>
<p>\(\text{0}\)</p>
</td>
<td>
<p>\(\text{1}\)</p>
</td>
<td>
<p>\(\text{2}\)</p>
</td>
</tr>
<tr>
<td>
<p>\(f(x)\)</p>
</td>
<td>
<p>\(-\text{2}\)</p>
</td>
<td>
<p>\(-\text{1}\)</p>
</td>
<td>
<p>\(\text{0}\)</p>
</td>
<td>
<p>\(\text{1}\)</p>
</td>
<td>
<p>\(\text{2}\)</p>
</td>
</tr>
</tbody>
</table>
</div>
<div>
<h3>Plot the points and join with a straight line curve</h3>
<p>From the table, we get the following points and the graph:</p>
<p>\((-2;-2), (-1;-1), (0;0), (1;1), (2;2)\)</p>
</div>
<div><img alt="ee0a220c8ea75bf1b6962835f9aa34e2.png" src="https://data.ulearngo.com/assets/2ffb2b18-b672-49e7-b7d5-b6b52f86c612"/></div>
<div>
<h3>Determine the domain and range</h3>
<p>Domain: \(x\in \mathbb{R}\)</p>
<p>Range: \(f(x)\in \mathbb{R}\)</p>
</div>
<div>
<h3>Determine the value of \(x\) for which \(f(x)=4\)</h3>
<p>From the graph we see that when \(f(x)=4\), \(x=4\). This gives the point \((4;4)\).</p>
</div>
<div>
<h3>Determine the intercept</h3>
<p>The function \(f\) intercepts the axes at the origin \((0;0)\).</p>
</div>
</div>
</div>
<section></section>

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Functions of the Form <em>y = x</em>

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Functions of the Form <em>y = x</em>

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