15. Q15b
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Similar Question 1
<p>Use the base function <code class='latex inline'>f(x)=x</code>. Write the equation for each transformed function. </p><p><code class='latex inline'>t(x)=f(x-11)+4</code></p>
Similar Question 2
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p> <code class='latex inline'>g(x)=\sqrt{x-9}-5</code></p>
Similar Question 3
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = \frac{2}{3}f(x + 3) + 1 </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>If <code class='latex inline'>f(x) = x^2</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y= 0.5f(3 (x - 4)) - 1</code></p>
<p>Describe the transformation that&#39;s indicated by the arrows.</p><img src="/qimages/864" />
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>t(x)=f(x+1)-11</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>\displaystyle{g(x)=\frac{1}{x}+5}</code></p>
<p>For <code class='latex inline'>f(x) = | x|</code>, sketch the graph of <code class='latex inline'>p(x) = f(4x + 8)</code>.</p>
<p>Given <code class='latex inline'>f(x)=x</code>, determine if there is a single horizontal translation that has the same effect as a single vertical translation. Justify your answer algebraically (with equations), numerically (with points), and graphically (with sketches). </p>
<p>Sketch each set of functions on the same set of axes.</p><p><code class='latex inline'>y = \frac{1}{x}, y = \frac{2}{x}, y = - \frac{2}{x}, y = -\frac{2}{x-1} + 3</code></p>
<p>If <code class='latex inline'>f(x) = x^2</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y= -f(\frac{1}{4}(x + 1)) + 2</code></p>
<p>The function <code class='latex inline'>y=f(x)</code> has been transformed to <code class='latex inline'>y=af[k(x - d)] + c</code>. Determine <code class='latex inline'>a, k, c,</code> and <code class='latex inline'>d</code>; sketch the graph and state the domain and range for each transformation.</p><p>A vertical compression by the factor <code class='latex inline'>\frac{1}{2}</code>, a reflection in the y-axis, a translation 3 units left, and a translation 4 units down are applied to <code class='latex inline'>f(x) = \frac{1}{x}</code>.</p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>t(x)=f(x+12)-3</code></p>
<p>If <code class='latex inline'>f(x) =| x |</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=2f(x - 3)</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>m(x)=f(x+6)</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>s(x)=f(x+5)+4</code></p>
<p>The graph of <code class='latex inline'>y=f(x)</code> is reflected in the <code class='latex inline'>y</code>-axis, stretched vertically by the factor 3, and then translated up 2 units and 1 unit left. Write the equation of the new function in terms of <code class='latex inline'>f</code>.</p>
<p>Use the base function <code class='latex inline'>f(x)=x</code>. Write the equation for each transformed function. </p><p><code class='latex inline'>r(x)=f(x+2)+9</code></p>
<p>Low and high blood pressure can both be dangerous. Doctors use a special index, <code class='latex inline'>P_d</code>, to measure how far from normal someone&#39;s blood pressure is. In the equation <code class='latex inline'>P_d = | P - \bar{P} |</code>, <code class='latex inline'>P</code> is a person&#39;s systolic blood pressure and <code class='latex inline'>\bar{P}</code> is the normal systolic blood pressure. Sketch the graph of this index. Assume that normal systolic blood pressure is 120mm(Hg).</p>
<p>Use the base function <code class='latex inline'>f(x)=\sqrt{x}</code>. Write the equation for each transformed function.</p><p><strong>(a)</strong> <code class='latex inline'>n(x)=f(x-4)-6</code></p><p><strong>(b)</strong> <code class='latex inline'>r(x)=f(x+2)+9</code></p><p><strong>(c)</strong> <code class='latex inline'>s(x)=f(x+6)-7</code></p><p><strong>(d)</strong> <code class='latex inline'>t(x)=f(x-11)+4</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>n(x)=f(x-3)+6</code></p>
<p>If <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'> y= -2f(-(x - 2)) + 1</code></p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p> <code class='latex inline'> \displaystyle y = \frac{1}{2x} </code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>h(x)=f(x-8)</code></p>
<p>The graph of <code class='latex inline'>g(x) = \sqrt{x}</code> is reflected across the <code class='latex inline'>y</code>-axis, stretched vertically by the factor 3, and then translated 5 units right and 2 units down. Draw the graph of the new function and write its equation.</p>
<p>Use the base function <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code>. Write the equation for each transformed function.</p><p><strong>(a)</strong> <code class='latex inline'>n(x)=f(x-4)-6</code></p><p><strong>(b)</strong> <code class='latex inline'>r(x)=f(x+2)+9</code></p><p><strong>(c)</strong> <code class='latex inline'>s(x)=f(x+6)-7</code></p><p><strong>(d)</strong> <code class='latex inline'>t(x)=f(x-11)+4</code></p>
<p>The function <code class='latex inline'>y=f(x)</code> has been transformed to <code class='latex inline'>y=af[k(x - d)] + c</code>. Determine <code class='latex inline'>a, k, c,</code> and <code class='latex inline'>d</code>; sketch the graph and state the domain and range for each transformation.</p><p>A vertical stretch by the factor 2, a reflection in the x-axis, and a translation 4 units right are applied to <code class='latex inline'>y=\sqrt{x}</code>.</p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p> <code class='latex inline'>g(x)=\sqrt{x-9}-5</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> y=-3f(2(x - 1)) - 3 </code></p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p><code class='latex inline'> \displaystyle y = 0.5(\frac{1}{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 traffic safety bureau receives data regarding acceleration of a prototype electric sports car. It can accelerate from 0 to 100 km/h in about 4 s. Its position, d, in metres, at any time t, in seconds, is given by <code class='latex inline'>d(t)=3.5t^2</code>. Mathew is comparing the prototype to a hybrid electric car, which has its position given by <code class='latex inline'>d(t)=1.4t^2</code>. </p><p><strong>(a)</strong> In a race between the two cars, the hybrid is given a head start. Where would the hybrid have to start so that after 4 s of acceleration, both cars are in the same position?</p>
<p>Use the base function <code class='latex inline'>f(x)=x</code>. Write the equation for each transformed function.</p><p><code class='latex inline'>n(x)=f(x-4)-6</code> </p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p><code class='latex inline'> \displaystyle y= \frac{2}{x} </code></p>
<img src="/qimages/864" /><p>Match the words with letters.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccc} &\text{Divide the x-coordinates by 3.} && A\\ &\text{Multiply the y-coordinates by 5.} && B\\ &\text{Multiply the x-coordinates by -1.} && C\\ &\text{Add 4 to the y-coordinates.} && D\\ &\text{Add 2 to the x-coordinates.} && E\\ \end{array} </code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=x+12</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=3f(x) - 1</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>b(x)=f(x)+5</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>h(x)=f(x-4)</code></p>
<p>The cost to produce<code class='latex inline'>x</code> units of a product can be modelled by the function <code class='latex inline'>c(x)=\sqrt{x}+500</code>. </p><p><strong>(b)</strong> Suppose that the cost to make 10 prototype units is to be included in the cost. Write a new function representing the cost of this product. </p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>g(x)=f(x)-6</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>m(x)=f(x-2)+10</code></p>
<p>If <code class='latex inline'>f(x) =| x |</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=-\frac{1}{2}f(3 (x + 2)) + 4</code></p>
<p>Use words and function notation to describe the transformation that can be applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. State the domain and range of each function. </p><img src="/qimages/801" />
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=(x-6)^2</code></p>
<p>If <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=f(-\frac{1}{2}(x + 4)) - 3 </code></p>
<p>Use the base function <code class='latex inline'>f(x)=x^2</code>. Write the equation for each transformed function.</p><p><strong>(a)</strong> <code class='latex inline'>n(x)=f(x-4)-6</code></p><p><strong>(b)</strong> <code class='latex inline'>r(x)=f(x+2)+9</code></p><p><strong>(c)</strong> <code class='latex inline'>s(x)=f(x+6)-7</code></p><p><strong>(d)</strong> <code class='latex inline'>t(x)=f(x-11)+4</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=x^2+8</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>n(x)=f(x+7)</code></p>
<p>Sketch each set of functions on the same set of axes.</p><p><code class='latex inline'>y=x^2, y = 3x^2, y = 3(x-2)^2 + 1</code></p>
<p>Use the base function <code class='latex inline'>f(x)=x</code>. Write the equation for each transformed function. </p><p><code class='latex inline'>t(x)=f(x-11)+4</code></p>
<p>Use words and function notation to describe the transformation that can be applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. State the domain and range of each function. </p><img src="/qimages/800" />
<p>The graph of <code class='latex inline'>f(x)=x^2</code> is transformed to the graph of <code class='latex inline'>g(x)=f(x+8)+12</code>.</p><p><strong>(b)</strong> Determine three points on the base function. Horizontally translate and then vertically translate the points to determine the image points on <code class='latex inline'>g(x)</code>.</p><p><strong>(c)</strong> Start with your original points, but this time reverse the order of your translations. Determine whether the order of the translations is important. </p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=f(2x) - 5</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p> <code class='latex inline'> \displaystyle y = 4f(-x) - 4 </code></p>
<p>The graphs of <code class='latex inline'>y=x^2</code> and another parabola are shown.</p><img src="/qimages/866" /><p><strong>(a)</strong> Determine a combination of transformations that would produce the second parabola from the first.</p><p><strong>(b)</strong> Determine a possible equation for the second parabola.</p>
<p>If <code class='latex inline'>f(x) = x^2</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=f(x - 2) + 3</code></p>
<p>Use words and function notation to describe the transformation that can be applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. State the domain and range of each function. </p><img src="/qimages/798" />
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p> <code class='latex inline'> \displaystyle y = -\frac{1}{x} </code></p>
<img src="/qimages/342" /><p><strong>(a)</strong> Copy and complete the table of values.</p><p><strong>(b)</strong> Use the points to graph all three functions on the same set of axes.</p><p><strong>(c)</strong> Explain how the points of the translated functions relate to the actual transformations. </p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=f(\frac{1}{3}(x + 4))</code></p>
<p>Sketch each set of functions on the same set of axes.</p><p><code class='latex inline'>y = \sqrt{x}, y = \sqrt{3x}, y = \sqrt{-3x}, y = \sqrt{-3(x + 1)} - 4</code></p>
<p>If <code class='latex inline'>f(x) =| x |</code>, sketch the graph of each function and state the domain and range.</p><p><code class='latex inline'>y=4f(2(x - 1)) - 2</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=\sqrt{x+10}</code></p>
<p>Complete the table for the point (1, 1).</p><p><code class='latex inline'>\displaystyle\begin{array}{|c|c|c|c|c|} f(x) &f(3x) &f(-3x) &5f(-3x) & 5f(-3(x-2))+4\\ -&- &-&-&-\\ (1, 1)&&&&\\ \end{array}</code></p>
<p>The cost to produce<code class='latex inline'>x</code> units of a product can be modelled by the function <code class='latex inline'>c(x)=\sqrt{x}+500</code>. </p><p><strong>(a)</strong> State and interpret the domain and range of the cost function.</p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = f(x - 2) + 3 </code></p>
<p>The traffic safety bureau receives data regarding acceleration of a prototype electric sports car. It can accelerate from 0 to 100 km/h in about 4 s. Its position, d, in metres, at any time t, in seconds, is given by <code class='latex inline'>d(t)=3.5t^2</code>. Mathew is comparing the prototype to a hybrid electric car, which has its position given by <code class='latex inline'>d(t)=1.4t^2</code>. </p><p><strong>(a)</strong> In a race between the two cars, the hybrid is given a head start. Where would the hybrid have to start so that after 4 s of acceleration, both cars are in the same position?</p><p><strong>(b)</strong> Verify your solution by graphing in part (a).</p>
<p>The graph of <code class='latex inline'>f(x)=x^2</code> is transformed to the graph of <code class='latex inline'>g(x)=f(x+8)+12</code>.</p><p>Describe the two transformations represented by this transformation.</p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=x-9</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(-\frac{1}{3}x)</code>.</p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>g(x)=\sqrt{x}-12</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'>y=2f( - (x - 3)) + 1</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>s(x)=f(x+8)+9</code></p>
<p>Match each equation to its graph. Explain your reasoning.</p><p><code class='latex inline'> \displaystyle \begin{array}{ccccccc} &(a)& y=\frac{3}{-(x - 2)} + 1 & (e)& y=-\frac{4}{x} - 3 \\ &(b)& y=2| x-3 | -2 & (f)& y= -0.5| x + 4 | + 2 \\ &(c)& y=-2\sqrt{ x+ 3} - 2 & (g)& y=-0.5\sqrt{1-x} + 1 \\ &(d)& y=(0.25(x-2))^2 - 3 & (h)& y=-\frac{1}{2}(x + 4)^2 + 1 \\ \end{array} </code></p><img src="/qimages/865" />
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = \frac{2}{3}f(x + 3) + 1 </code></p>
<p>Use the base function <code class='latex inline'>f(x)=x</code>. Write the equation for each transformed function. </p><p><code class='latex inline'>s(x)=f(x+6)-7</code></p>
<p>Explain what transformations you would need to apply to the graph of <code class='latex inline'>y=f(x)</code> to graph each function.</p><p><code class='latex inline'> \displaystyle y = -f(\frac{1}{2}x) -2 </code></p>
<p>Bob uses the relationship <code class='latex inline'>Time = \frac{Distance}{Speed}</code> to plan his kayaking trips. Tomorrow Bob plans to kayak 20 km across a calm lake. He wants to graph the relation <code class='latex inline'>T(s) = \frac{20}{s}</code> to see how the time, <code class='latex inline'>T</code>, it will take varies with his kayaking speed, <code class='latex inline'>s</code>. The next day, he will kayak 15 km up a river that flows at 3 km/h. He will need the graph of <code class='latex inline'>\displaystyle T(s) = \frac{15}{s - 3}</code> to plan this trip. Use transformations to sketch both graphs.</p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>r(x)=f(x-5)-9</code></p>
<p>The cost to produce<code class='latex inline'>x</code> units of a product can be modelled by the function <code class='latex inline'>c(x)=\sqrt{x}+500</code>. </p><p><strong>(c)</strong> What type of transformation does the change in part (b) represent?</p><p><strong>(d)</strong> How does the transformation in part (b) affect the domain and range?</p>
<p>For <code class='latex inline'>f(x) = \sqrt{x}</code>, sketch the graph of <code class='latex inline'>h(x) = f(-3x - 12)</code>.</p>
<p>Describe the transformations that you would apply to the graph of <code class='latex inline'>f(x) = \frac{1}{x}</code> to transform it into each of these graphs.</p><p><code class='latex inline'> \displaystyle y = \frac{1}{x -2} </code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>g(x)=f(x)-7</code></p>
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, D&#39;, E&#39;, and F&#39; from the vertices of the graph below.</p><img src="/qimages/796" /><p><code class='latex inline'>r(x)=f(x-2)-10</code></p>
<p>For <code class='latex inline'>f(x) = x^2</code>, sketch the graph of <code class='latex inline'>g(x) = f(2x + 6)</code>.</p>
<p>Compare the graphs and the domains and ranges of <code class='latex inline'>f(x) = x^2</code> and <code class='latex inline'>g(x) = \sqrt{x}</code>. How are they alike? How are they different? Develop a procedure to obtain the graph of <code class='latex inline'>g(x)</code> from the graph of <code class='latex inline'>f(x)</code>.</p>
<p>Use words and function notation to describe the transformation that can be applied to the graph of <code class='latex inline'>f(x)</code> to obtain the graph of <code class='latex inline'>g(x)</code>. State the domain and range of each function. </p><img src="/qimages/802" />
<p>Copy the graph of <code class='latex inline'>f(x)</code>. Apply each transformation by determining the image points A&#39;, B&#39;, C&#39;, and D&#39;.</p><img src="/qimages/797" /><p><code class='latex inline'>b(x)=f(x)+3</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>\displaystyle{g(x)=\frac{1}{x+3}-8}</code></p>
<p>For each function <code class='latex inline'>g(x)</code>, identify the base function as one of <code class='latex inline'>f(x)=x</code>, <code class='latex inline'>f(x)=x^2</code>, <code class='latex inline'>f(x)=\sqrt{x}</code>, and <code class='latex inline'>\displaystyle{f(x)=\frac{1}{x}}</code> and describe the transformation first in the form <code class='latex inline'>y=f(x-d)+c</code> and then in words. Transform the graph of <code class='latex inline'>f(x)</code> to sketch the graph of <code class='latex inline'>g(x)</code> and then state the domain and range of each function.</p><p><code class='latex inline'>\displaystyle{g(x)=\frac{1}{x-2}}</code></p>
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