18. Q18
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Similar Question 1
<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" />
Similar Question 2
<p>Use the base function <code class='latex inline'>f(x) = x^{2}</code>. Write the equation for each transformed function. </p><p>a) <code class='latex inline'>b(x) = f(x + 2)</code><br> b) <code class='latex inline'>h(x) = f(x) - 5</code><br> c) <code class='latex inline'>m(x) = f(x) + 9</code><br> d) <code class='latex inline'>n(x) = f(x - 3) - 7</code><br> e) <code class='latex inline'>r(x) = f(x + 4) + 6</code><br> f) <code class='latex inline'>s(x) = f(x + 2) - 8</code><br> g) <code class='latex inline'>t(x) = f(x - 5) + 1</code></p>
Similar Question 3
<p>For each graph, state the domain and range in set notation. The scale on both axes is 1 unit per tick mark in each calculator screen.</p><img src="/qimages/77897" />
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>Use a graphing calculator or graphing software to graph each function. State its domain and range. <code class='latex inline'>\displaystyle f(x)=-2 x^{2}+5 </code></p><p>where <code class='latex inline'>\displaystyle x \geq 0 </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>Describe, in the appropriate order, the transformations that must be applied to the base function <code class='latex inline'>f(x)</code> to obtain the transformed function. </p><p>Then, write the corresponding equation and transform the graph of f(x] to sketch the graph of g(x).</p><p><code class='latex inline'>f(x) =x^2</code><br> <code class='latex inline'>g(x) = f[\frac{1}{2}(x+1)]</code></p>
<p>For each function f(x), determine the equation for g(x).</p><p><code class='latex inline'>f(x) = (x - 3)^2 + 10</code></p><p><code class='latex inline'>g(x) = -f(-x)</code></p>
<p>Determine <code class='latex inline'>\displaystyle f(-2), f(0), f(2) </code>, and <code class='latex inline'>\displaystyle f(2 x) </code> for each function.</p><p><code class='latex inline'>\displaystyle f(x)=-3 x^{2}+5 </code></p>
<p>a) Create a table of values for the function <code class='latex inline'>\displaystyle f(x)=-x^{2}+5 x+2 </code> for the domain <code class='latex inline'>\displaystyle \{-2,-1,0,1,2,3,4,5,6,7\} . </code> b) Graph this quadratic function.</p><p>c) On the same set of axes, graph the</p><p>line <code class='latex inline'>\displaystyle y=4 </code>.</p><p>d) Use your graph to estimate the</p><p><code class='latex inline'>\displaystyle x </code>-values of the points of intersection of <code class='latex inline'>\displaystyle y=4 </code> and <code class='latex inline'>\displaystyle f(x)=-x^{2}+5 x+2 . </code> e) Determine the coordinates of</p><p>the points of intersection of</p><p><code class='latex inline'>\displaystyle f(x)=-x^{2}+5 x+2 </code> and <code class='latex inline'>\displaystyle y=4 </code> algebraically.</p>
<p>Given <code class='latex inline'>f(x) = 2x^2 -2x, -2 \leq x \leq 3</code> and <code class='latex inline'>g(x) = -4x, -3 \leq x \leq 5</code>, graph the following.</p><p><code class='latex inline'>f</code></p>
<p>For each function g(x), describe the transformation from a base function 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>, or <code class='latex inline'>f(x) = \dfrac{1}{x}</code>. Then transform the graph of f(x) to sketch a graph of g(x).</p><p><code class='latex inline'>g(x) = (5x)^2</code></p>
<p>Find the domain and range of each function. Explain your answers. <code class='latex inline'>\displaystyle f(x)=2 x^{2}+4 x+7 </code></p>
<p>For each function, identify the base function as one of <code class='latex inline'>f(x) = x, f(x) = x^2, f(x) = \sqrt{x}</code>, or <code class='latex inline'>f(x) = \frac{1}{x}</code>. Sketch the graphs of the base function and the transformed function, and state the domain and range of the functions. </p><p><code class='latex inline'>e(x) = 4x^2 - 3</code></p>
<p>A quadratic function of the form</p><p><code class='latex inline'>\displaystyle f(x)=a x^{2}+b x+c </code> satisfies the conditions <code class='latex inline'>\displaystyle f(1)=4, f(-1)=10 </code>, and <code class='latex inline'>\displaystyle f(2)=7 </code>. Determine the values of <code class='latex inline'>\displaystyle a, b </code> and <code class='latex inline'>\displaystyle c </code>, and state the defining equation.</p>
<p>Find the value of each function at <code class='latex inline'>\displaystyle x=0 . </code> Sketch the graph of each function.</p><p>d) <code class='latex inline'>\displaystyle g(x)=10 x^{2}+4 x-1 </code></p>
<p>If <code class='latex inline'>f(x) = 3(x+ 2)^2-5</code>, the domain must be restricted to which interval if the inverse is to be a function?</p><p>a) <code class='latex inline'>x \geq -5</code></p><p>b) <code class='latex inline'>x \geq -2</code></p><p>c) <code class='latex inline'>x \geq 2</code></p><p>d) <code class='latex inline'>x \geq 5</code></p>
<p>Complete the square to express each function in vertex form. Then graph each, and state the domain and range.</p><p><code class='latex inline'> \displaystyle f(x) = x^2 + 8x + 13 </code></p>
<p>Complete the square to express each function in vertex form. Then graph each, and state the domain and range.</p><p><code class='latex inline'> \displaystyle f(x) =-x^2 + 2x -7 </code></p>
<p>For each function, determine the range for the domain {—2, —1, 0, 1. 2}.</p><p><code class='latex inline'>\displaystyle y = -(x + 3)^2 - 2 </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) = (x - 1)^{2} + 11</code><br> <code class='latex inline'>g(x) = -f(-x)</code></p>
<p>State whether each relation is quadratic. Justify your answer.</p><p><code class='latex inline'>\displaystyle y - 5x^2 + 3x- 1 </code></p>
<p>Complete the square to express each function in vertex form. Then graph each, and state the domain and range.</p><p><code class='latex inline'> \displaystyle f(x) = -3x^2 -12x - 11 </code></p>
<p>For each graph, state the domain and range in set notation. The scale on both axes is 1 unit per tick mark in each calculator screen.</p><img src="/qimages/77893" />
<p>For each function below,</p><p>i) determine <code class='latex inline'>\displaystyle f(-2), f(1) </code>, and <code class='latex inline'>\displaystyle f\left(\frac{1}{2}\right) </code> ii) write the function in mapping</p><p>notation</p><p>c) <code class='latex inline'>\displaystyle f(x)=-3(x+1)^{2}-2 </code></p>
<p>For each function <code class='latex inline'>g(x)</code>, describe the transformation from a base function of <code class='latex inline'>f(x) = x, f(x) = x^2, f(x) = \sqrt{x}</code>, or <code class='latex inline'>f(x) = \frac{1}{x}</code>. Then skctch a graph of <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code> on the same axes.</p><p><code class='latex inline'>g(x) = (4x)^2</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>a) <code class='latex inline'>b(x) = f(x + 2)</code><br> b) <code class='latex inline'>h(x) = f(x) - 5</code><br> c) <code class='latex inline'>m(x) = f(x) + 9</code><br> d) <code class='latex inline'>n(x) = f(x - 3) - 7</code><br> e) <code class='latex inline'>r(x) = f(x + 4) + 6</code><br> f) <code class='latex inline'>s(x) = f(x + 2) - 8</code><br> g) <code class='latex inline'>t(x) = f(x - 5) + 1</code></p>
<p>The same quadratic function fix) can be expressed in three different forms:</p> <ul> <li><code class='latex inline'> \displaystyle f(x) = (x - 7)^2 - 25 </code></li> <li><code class='latex inline'> \displaystyle f(x) = x^2 -14x + 24 </code></li> <li><code class='latex inline'> \displaystyle f(x) = (x - 12)(x - 2) </code></li> </ul> <p>What information about the parabola does each form provide?</p>
<p>State whether each relation is quadratic. Justify your answer.</p><img src="/qimages/9870" />
<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>Find the value of each function at <code class='latex inline'>\displaystyle x=0 . </code> Sketch the graph of each function.</p><p>f) <code class='latex inline'>\displaystyle q(x)=-\frac{1}{2}(3-4 x)(x-5) </code></p>
<p>Determine an equation for this quadratic relation.</p><img src="/qimages/9874" />
<p>Write each function in mapping notation.</p><p>b) <code class='latex inline'>\displaystyle g(x)=x^{2}+7 x-5 </code></p>
<p>State the vertex, the equation of the axis of symmetry, and the domain and range.</p><p>a) <code class='latex inline'>\displaystyle f(x) = -3(x - 2)^2 + 5 </code></p><p>b) <code class='latex inline'>\displaystyle f(x) = 2(x + 4)(x -6) </code></p>
<p>Use a graphing calculator or graphing software to graph each function. State its domain and range. <code class='latex inline'>\displaystyle g(x)=x^{2}-6 x+2 </code></p>
<p>For each function below,</p><p>i) determine <code class='latex inline'>\displaystyle f(-2), f(1) </code>, and <code class='latex inline'>\displaystyle f\left(\frac{1}{2}\right) </code> ii) write the function in mapping</p><p>notation</p><p>b) <code class='latex inline'>\displaystyle f(x)=6 x^{2}-4 x+3 </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>Without graphing, predict how the graphs of the equations in each pair will differ. Explain your reasoning.</p><p><code class='latex inline'>\displaystyle y = x^2 -4x + 3 </code> and <code class='latex inline'>\displaystyle y = x^2 -4x </code></p>
<p>Consider the function <code class='latex inline'>\displaystyle f(x)=s^{2}-6 s+9 </code></p><p>a) Determine each value.</p> <ul> <li><p>i) <code class='latex inline'>\displaystyle f(0) </code></p></li> <li><p>iv) <code class='latex inline'>\displaystyle f(3) </code></p></li> <li><p>ii) <code class='latex inline'>\displaystyle f(1) </code></p></li> <li><p>v) <code class='latex inline'>\displaystyle [f(2)-f(1)]-[f(1)-f(0)] </code></p></li> <li><p>iii) <code class='latex inline'>\displaystyle f(2) </code></p></li> <li><p>vi) <code class='latex inline'>\displaystyle [f(3)-f(2)]-[f(2)-f(1)] </code></p></li> </ul> <p>b) In part (a), what are the answers to (v) and (vi) commonly called?</p>
<p>Describe the transformations that were applied to <code class='latex inline'>y = x^2</code> to obtain each of the following functions.</p><p><code class='latex inline'>y =40(-7(x - 10))^2 + 9 </code></p>
<p>Give an example of an equation of a quadratic relation whose vertex and x—intercept occur at the same point.</p>
<p>For each function, identify the base function as one of <code class='latex inline'>f(x) = x, f(x) = x^2, f(x) = \sqrt{x}</code>, or <code class='latex inline'>f(x) = \frac{1}{x}</code>. Sketch the graphs of the base function and the transformed function, and state the domain and range of the functions. </p><p><code class='latex inline'>h(x) = (3x + 18)^2</code></p>
<p>Evaluate for the given x-values.</p><p><code class='latex inline'>\displaystyle f(x)=3 x^{2}-4 ; x=0, x=4 </code></p>
<p>Identify the intervals of increase/decrease, the symmetry, and the domain and range of each function.</p><p><code class='latex inline'>\displaystyle f(x) = x^2+ 2 </code></p>
<p>Complete the square to express each function in vertex form. Then graph each, and state the domain and range.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 12x + 19 </code></p>
<p>Use a graphing calculator or graphing software to graph each function. State its domain and range. <code class='latex inline'>\displaystyle g(t)=2+t-10 t^{2} </code></p>
<p>Sketch the graph of each equation by correctly applying the required transformation(s) to points on the graph of <code class='latex inline'>y = x^2</code>. State the transformation mapping.</p><p><code class='latex inline'> \displaystyle y = 2x^2 </code></p>
<p>For the quadratic function <code class='latex inline'>g(x) = 4x^2 -24x + 31</code></p><p>a) Write the equation in vertex form.</p><p>b) Write the equation of the axis of symmetry</p><p>c) Write the coordinates of the vertex.</p><p>d) Determine the maximum or minimum value of g(x). State a reason for your choice.</p><p>e) Determine the domain of g(x).</p><p>f) Determine the range of g(x).</p><p>g) Graph the function.</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)=(x+1)^2-4</code>, <code class='latex inline'>g(x)=f(-x)</code></p>
<p>Given each graph of <code class='latex inline'>f(x)</code>, graph and label <code class='latex inline'>g(x)</code>. </p><p><code class='latex inline'>g(x) = f(3x)</code></p><img src="/qimages/24525" />
<p>Evaluate for the given x-values. <code class='latex inline'>\displaystyle f(x)=2 x^{2}+5 ; x=2, x=3 </code></p>
<p>Use a graphing calculator or graphing software to graph each function. State its domain and range.</p><p><code class='latex inline'>\displaystyle h(x)=3 x^{2}-14 x-5 </code>,</p><p>where <code class='latex inline'>\displaystyle x \geq 0 </code></p>
<p>Determine <code class='latex inline'>\displaystyle f(-2), f(0), f(2) </code>, and <code class='latex inline'>\displaystyle f(2 x) </code> for each function. <code class='latex inline'>\displaystyle f(x)=4 x^{2}-2 x+1 </code></p>
<p>For each graph, state the domain and range in set notation. The scale on both axes is 1 unit per tick mark in each calculator screen.</p><img src="/qimages/77897" />
<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>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>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>Given each base function f(x), write the equation of the transformed function g(x). Then transform the graph of f(x) to sketch a graph of g(x).</p><p><code class='latex inline'>f(x) = x^2</code></p><p><code class='latex inline'>g(x) = f[\dfrac{1}{4}(x + 5)]</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(x - 2) + 3</code></p>
<p>State the domain and range of the quadratic function represented by the following table of values.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline \boldsymbol{y} & 12 & 20 & 27 & 32 & 35 & 36 & 35 & 32 & 27 & 20 & 12 \\ \hline \end{array} </code></p>
<p>Determine the domain and the range of each function.</p><p><code class='latex inline'>\displaystyle y=-(x-3)^{2}+2 </code></p>
<p>Find the value of each function at <code class='latex inline'>\displaystyle x=0 . </code> Sketch the graph of each function.</p><p>e) <code class='latex inline'>\displaystyle h(x)=(5 x-2)(3 x+6) </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) = (x + 8)^{2} - 17</code><br> <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)=(x-5)^2+9</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/804" />
<p>Describe the transformations that were applied to <code class='latex inline'>y = x^2</code> to obtain each of the following functions.</p><p><code class='latex inline'>y = -2(x -1)^2 + 23</code></p>
<p>The height of a flare is a function of the elapsed time since it was fired. An expression for its height is <code class='latex inline'>\displaystyle f(t)=-5 t^{2}+100 t </code>. Express the domain and range of this function in set notation. Explain your answers.</p>
<p>Determine the range of each function for the domain <code class='latex inline'>\displaystyle \{-2,-1,0,1,2\} </code></p><p><code class='latex inline'>y = 2x^2 -7</code></p>
<p>Complete the square to express each function in vertex form. Then graph each, and state the domain and range.</p><p><code class='latex inline'> \displaystyle f(x) = \frac{1}{2}x^2 + 3x + 4 </code></p>
<p>State the domain and range of the relation. Then determine whether the relation is a function. State domain and range.</p><p><code class='latex inline'>y = -5x^2</code></p>
<p>Find the domain and range of each function. Explain your answers. <code class='latex inline'>\displaystyle f(x)=-2(x+3)^{2}+5 </code></p>
<p>For <code class='latex inline'>\displaystyle h(x) = 3x^2 -24x + 50 </code></p><p>find </p><p>i. the domain and range.</p><p>ii. the relationship to the parent function. including all applied transformations</p><p>iii. a sketch of the function</p>
<p>Describe the transformations that were applied to <code class='latex inline'>y = x^2</code> to obtain each of the following functions.</p><p><code class='latex inline'>y = (\frac{12}{13}(x + 9))^2 - 14</code></p>
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