<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>11.7.1b circle example</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<hr>
<h4 class="HELM_example">Example</h4>
<p>Sketch the graphs of \( f_1(x) =  \sqrt{1 - x^2} \) and \( f_2(x) = - \sqrt{1 - x^2} \).</p>
<h4 class="HELM_solution">Solution</h4>
<p>Since \(x^2 + y^2 = 1\) is the well-known equation of the circle with centre at the origin and radius \(1\), it follows that the graphs of \(f_1(x)\) and \(f_2(x)\) are the upper and lower halves of this circle.
</p><p style="text-align: center;"><img src="@@PLUGINFILE@@/11-7%20circle.svg" alt="unit circle" width="451" height="153" class="img-responsive atto_image_button_text-bottom"><br></p>
<hr>
<p></p>
Sometimes it is difficult or even impossible to solve an equation in \(x\) and \(y\) to obtain \(y\) explicitly in terms of \(x\).
<p></p>
Examples where explicit expressions for \(y\) cannot be obtained are
\[\sin(xy) = y\]
and
\[x^2 + \sin y = 2y.\]]]></text>
<file name="11-7 circle.svg" path="/" encoding="base64">[encoded data, 12032 characters]</file>
<file name="11.6 fig 9 tangent.svg" path="/" encoding="base64">[encoded data, 8576 characters]</file>
    </questiontext>
    <generalfeedback format="html">
      <text/>
    </generalfeedback>
    <defaultgrade>0</defaultgrade>
    <penalty>0</penalty>
    <hidden>0</hidden>
    <idnumber/>
  </question>
</quiz>
