3. Q3b
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Similar Question 1
<p>The graph of <code class='latex inline'>y=x^2</code> opens up and the graph of <code class='latex inline'>y=-x^2</code> opens down. How would you compare the graphs of the following pairs of equations?</p><p><strong>(a)</strong> <code class='latex inline'>y=\sqrt{x}</code> and <code class='latex inline'>y=-\sqrt{x}</code></p><p><strong>(b)</strong><code class='latex inline'>y=|x|</code> and <code class='latex inline'>y=-|x|</code></p><p><strong>(c)</strong> <code class='latex inline'>y=\frac{1}{x}</code> and <code class='latex inline'>y=-\frac{1}{x}</code></p>
Similar Question 2
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/807" />
Similar Question 3
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\frac{1}{x-3}-6</code>, <code class='latex inline'>g(x)=-f(-x)</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=-\sqrt{x-2}+5</code>, <code class='latex inline'>g(x)=f(-x)</code></p>
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/804" />
<p>Sketch the graph of <code class='latex inline'>f(x)=\sqrt{x}</code> reflected in: </p><p> <code class='latex inline'>x=4</code></p>
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p><strong>(b)</strong> Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p><strong>(c)</strong> Sketch the graphs of all four functions on the same set of axes.</p><p><strong>(d)</strong> State the domain and range of each function. Describe any similarities or differences. Refer the parts (a), (b), (c)</p>
<p>For each graph, describe the reflection that transforms <code class='latex inline'>f(x)</code> into <code class='latex inline'>g(x)</code>. </p><img src="/qimages/381" />
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/803" />
<p>The point <code class='latex inline'>(m,n)</code> is reflected in the <code class='latex inline'>x</code>-axis and then the image is reflected in the <code class='latex inline'>y</code>-axis. What is the <code class='latex inline'>y</code>-intercept of the line joining the original point and the final reflected point?</p>
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/803" />
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\sqrt{x+4}-4</code>, <code class='latex inline'>g(x)=-f(x)</code></p>
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/807" />
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p><strong>(b)</strong> Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p><strong>(c)</strong> Sketch the graphs of all four functions on the same set of axes.</p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing. </p><p><code class='latex inline'>f(x)=\sqrt{x-10}+3</code>, <code class='latex inline'>g(x)=-\sqrt{x-10}+3</code></p>
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/805" />
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=(x+1)^2-4</code>, <code class='latex inline'>g(x)=f(-x)</code></p>
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\sqrt{x+9}-1</code>, <code class='latex inline'>g(x)=-f(-x)</code></p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/808" />
<p>Sketch the graph of $f(x)=\sqrt{x}$ reflected in: </p><p>(b) <code class='latex inline'>y=x</code></p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing.</p><p><code class='latex inline'>f(x)=\sqrt{x}</code>, <code class='latex inline'>g(x)=\sqrt{-x}</code></p>
<p>If <code class='latex inline'>f(x) = (x - 2)(x + 5)</code>, determine the x-intercepts for the function <code class='latex inline'> y=f(-(x + 2))</code>.</p>
<p>The graph of <code class='latex inline'>y=x^2</code> opens up and the graph of <code class='latex inline'>y=-x^2</code> opens down. How would you compare the graphs of the following pairs of equations?</p><p><strong>(a)</strong> <code class='latex inline'>y=\sqrt{x}</code> and <code class='latex inline'>y=-\sqrt{x}</code></p><p><strong>(b)</strong><code class='latex inline'>y=|x|</code> and <code class='latex inline'>y=-|x|</code></p><p><strong>(c)</strong> <code class='latex inline'>y=\frac{1}{x}</code> and <code class='latex inline'>y=-\frac{1}{x}</code></p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/805" />
<p>Determine whether there are translations and reflections that have equal effects.</p><p><strong>(a)</strong> Graph the function <code class='latex inline'>f(x)=(x-4)^2</code>.</p><p><strong>(b)</strong> Graph the reflection of <code class='latex inline'>f(x)</code> in the <code class='latex inline'>y</code>-axis.</p><p><strong>(c)</strong> Determine a translation that can be applied to <code class='latex inline'>f(x)</code> that has the same effect as the reflection in part (b)</p><p><strong>(d)</strong> Verify algebraically that the transformations in part (b) and (c) are the same.</p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/804" />
<p>Describe any patterns that you notice about how the domain and range are affected by reflections in the <code class='latex inline'>x</code> and <code class='latex inline'>y</code>-axes. Use specific examples to support your answer.</p>
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/808" />
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing.</p><p><code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>g(x)=(-x)^2</code></p>
<p>For each graph, describe the reflection that transforms <code class='latex inline'>f(x)</code> into <code class='latex inline'>g(x)</code>. </p><img src="/qimages/382" />
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing. </p><p><code class='latex inline'>f(x)=\frac{1}{x+7}</code>, <code class='latex inline'>g(x)=\frac{1}{-x+7}</code></p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/807" />
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/808" />
<p>Determine whether there are translations and reflections that have equal effects.</p><p><strong>(a)</strong> Graph the function <code class='latex inline'>f(x)=(x-4)^2</code>.</p><p><strong>(b)</strong> Graph the reflection of <code class='latex inline'>f(x)</code> in the <code class='latex inline'>y</code>-axis.</p>
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=\frac{1}{x-3}-6</code>, <code class='latex inline'>g(x)=-f(-x)</code></p>
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/803" />
<p>For each function <code class='latex inline'>f(x)</code>, determine the equation for <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>f(x)=(x-5)^2+9</code>, <code class='latex inline'>g(x)=-f(-x)</code></p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing. </p><p> <code class='latex inline'>f(x)=\frac{1}{x}</code>, <code class='latex inline'>g(x)=-\frac{1}{x}</code></p>
<p>Determine algebraically whether <code class='latex inline'>g(x)</code> is a reflection of <code class='latex inline'>f(x)</code> in each case. Verify your answer by graphing. </p><p><code class='latex inline'>f(x)=(x+5)^2+4</code>, <code class='latex inline'>g(x)=-(x+5)^2-4</code></p>
<p>Sketch the graph of the function <code class='latex inline'>k(x)=-f(-x)</code>. Then, state the domain and range of each function.</p><img src="/qimages/804" />
<p>For each graph, describe the reflection that transforms <code class='latex inline'>f(x)</code> into <code class='latex inline'>g(x)</code>. </p><img src="/qimages/380" />
<p><code class='latex inline'>f(x)=\sqrt{x+2}+3</code></p><p>(b) Write the equations for <code class='latex inline'>-f(x)</code>, <code class='latex inline'>f(-x)</code>, and <code class='latex inline'>-f(-x)</code>. Describe the transformation(s) represented by each equation.</p><p>(c) Sketch the graphs of all four functions on the same set of axes.</p><p>(d) State the domain and range of each function. Describe any similarities or differences. </p><p>(e) Are any points invariant? Explain. Refer the parts (a), (b), (c), (d)</p>
<p>Copy each graph of <code class='latex inline'>f(x)</code> and sketch its reflection in the <code class='latex inline'>x</code>-axis, <code class='latex inline'>g(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/806" />
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/805" />
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/807" />
<p>Sketch the graph of its reflection in the <code class='latex inline'>y-</code>axis, <code class='latex inline'>h(x)</code>. Then, state the domain and range of each function. </p><img src="/qimages/806" />
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