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Similar Question 1
<p>The function <code class='latex inline'>\displaystyle y=x^{2}+2 </code> has a domain <code class='latex inline'>\displaystyle \{-2,-1,0,1,2\} . </code> Find the range.</p>
Similar Question 2
<p>Determine whether each relation is a function.</p><img src="/qimages/38366" />
Similar Question 3
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(0,2),(1,5)(3,11),(4,14),(5,15)\} </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>Determine whether each relation is a function.</p><img src="/qimages/12329" />
<p>Find the range of <code class='latex inline'>f(x) = \frac{3}{x}</code>.</p>
<ol> <li>State the domain and the range for each relation. Determine if each relation is a function.</li> </ol> <img src="/qimages/17792" />
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(-1,1),(-1,2),(-1,3),(-1,4)\} </code></p>
<p>Determine whether each relation is a function. Explain.</p><p><code class='latex inline'>\displaystyle \{(2,2),(-1,5),(5,2),(2,-4)\} </code></p>
<p>Use the vertical line test to determine whether the relation is a function.</p><img src="/qimages/55068" />
<p>Evaluate <code class='latex inline'>\displaystyle f(3) </code> for each of the following.</p><p> <code class='latex inline'>\displaystyle \{(1,2),(2,0),(3,1),(4,2)\} </code></p>
<p>Is the relation a function? Why or why not?</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|} \hline \text{Number of Drivers }, x & \text{Number of Speeding Tickets}, \boldsymbol{y} \\ \hline 1 & 6 \\ \hline 1 & 4 \\ \hline 2 & 3 \\ \hline 7 & 8 \\ \hline \end{array} </code></p>
<img src="/qimages/43244" /><p>ATTENDING TO PRECISION The graph represents a function. Find the input value corresponding to an output of <code class='latex inline'>\displaystyle 2 . </code></p>
<p>State the domain and range of each relation. Then determine whether the relation is a function, and justify your answer.</p><img src="/qimages/85" />
<p>Determine whether each relation is a function, and state its domain and range.</p><p><code class='latex inline'>\displaystyle 3x^2 + 2y =6 </code></p>
<p>Determine whether each relation is a function, and state its domain and range.</p><p><code class='latex inline'>\displaystyle y = 2x + 3 </code></p>
<p>Evaluate the function <code class='latex inline'>\displaystyle f(x)=3 x^{2}-3 x+1 </code> at the given values.</p><p>a) <code class='latex inline'>\displaystyle f(-1) </code></p><p>b) <code class='latex inline'>\displaystyle f(3) </code></p><p>c) <code class='latex inline'>\displaystyle f(0.5) </code></p>
<p>If <code class='latex inline'>\displaystyle f(-2)=6 </code>, what point must be on the graph of <code class='latex inline'>\displaystyle f </code> ? Explain.</p>
<p>Determine the domain and range for each of the following and state whether it is a function:</p><p><code class='latex inline'>\displaystyle f(x) = 3x + 1 </code></p>
<p>State which of the following are graphs of functions.</p><img src="/qimages/63849" />
<p>Is the relation in the graph shown</p><p>at the right a function? Use the</p><p>vertical line test.</p><img src="/qimages/55055" />
<p>If a company&#39;s profit or loss depends on the number of items sold, which is the most reasonable set of values for the domain in this relation? Explain.</p><p>a) negative integers</p><p>b) positive integers</p><p>c) integers between <code class='latex inline'>\displaystyle -1500 </code> and 1500</p>
<p>If <code class='latex inline'>\displaystyle f(x)=-2 x-3 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}+5 x </code>, find each value.</p><p><code class='latex inline'>\displaystyle g(-3) </code></p>
<p>Which of these relations is not a function of <code class='latex inline'>\displaystyle x </code> ? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { a) } x=-y^{2} & \text { c) } y=\sqrt{x-3} \\ \text { b) } y=2 x^{2} & \text { d) } x+y=3\end{array} </code></p>
<p>Determine the function that describe the following function rules. Show your work.</p> <ul> <li>The sum of the input and output is 5.</li> </ul>
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/12964" />
<p>State which of the following are graphs of functions.</p><img src="/qimages/63848" />
<p>Find the domain and range of each relation, and determine whether it is a function.</p><img src="/qimages/88489" />
<p>Identify the domain and range of the relation <code class='latex inline'>\displaystyle \{(-2,3),(-1,4),(0,5),(1,6)\} . </code> Represent the relation with a mapping diagram. Is the relation a function?</p>
<ol> <li>Communication Is the set of ordered pairs <code class='latex inline'>\displaystyle (f, l) </code> a function, if <code class='latex inline'>\displaystyle f </code> is the first name of a person in your school and <code class='latex inline'>\displaystyle l </code> is the last name of the person? Explain.</li> </ol>
<p>If the point <code class='latex inline'>\displaystyle (2,6) </code> is on the graph of <code class='latex inline'>\displaystyle y=f(x) </code>, what is the value of <code class='latex inline'>\displaystyle f(2) </code> ? Explain.</p>
<img src="/qimages/24632" /><p>State the domain and range of the relation.</p><p>A. D 􏰻 {0, 2, 4}; R 􏰻 {􏰸-4, -􏰸2, 0, 2, 4}</p><p>B. D 􏰻 {􏰸-4, -􏰸2, 0, 2, 4}; R 􏰻 {0, 2, 4}</p><p>C. D 􏰻 {0, 2, 4}; R 􏰻 {􏰸-4, -􏰸2, 0}</p><p>D. D 􏰻 {􏰸-4, -􏰸2, 0, 2, 4}; R 􏰻 {-􏰸4, -􏰸2, 0, 2, 4}</p>
<p>If <code class='latex inline'>\displaystyle f(x)=-2 x-3 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}+5 x </code>, find each value.</p><p><code class='latex inline'>\displaystyle g(-6 m) </code></p>
<p>For each given domain and range, draw two relations on the same axes: one that is a function and one that is not a function.</p> <ul> <li>domain <code class='latex inline'>\{x\in \mathbb{R}\}</code></li> <li>range <code class='latex inline'>\{y\in \mathbb{R}\}</code></li> </ul>
<p>Consider the relation between <code class='latex inline'>x</code> and <code class='latex inline'>y</code> that consists of all points <code class='latex inline'>(x, y)</code> such that the distance from <code class='latex inline'>(x, y)</code> to the origin is <code class='latex inline'>5</code>.</p><p><strong>(a)</strong> Is <code class='latex inline'>(4, 3)</code> in the relation? Explain.</p><p><strong>(b)</strong> Is <code class='latex inline'>(1, 5)</code> in the relation? Explain.</p><p><strong>(c)</strong> Is the relation a function? Explain.</p>
<p>State the domain and range of the relation. Then determine whether the relation is a function, and justify your answer.</p><p><code class='latex inline'> \displaystyle y = 2^{-x} </code></p>
<p>If <code class='latex inline'>f(x)=3x-2</code> and <code class='latex inline'>g(x)=x^2-5</code>, find each value.</p><p>`\$2[f(6)]</p>
<p>Determine whether each relation is a function, and state its domain and range.</p><img src="/qimages/7281" />
<p>The function <code class='latex inline'>\displaystyle y=x^{2}+2 </code> has a domain <code class='latex inline'>\displaystyle \{-2,-1,0,1,2\} . </code> Find the range.</p>
<p>Find each value if <code class='latex inline'>\displaystyle f(x)=3 x+2, g(x)=-2 x^{2} </code>, and <code class='latex inline'>\displaystyle h(x)=-4 x^{2}-2 x+5 </code></p><p><code class='latex inline'>\displaystyle g(-3) </code></p>
<p>Graph each relation.Find the domain and range. </p><p><code class='latex inline'>\displaystyle \{(0,1),(1,-3),(-2,-3),(3,-3)\} </code></p>
<p>State the <code class='latex inline'>y</code>-intercept of each quadratic relation.</p> <ul> <li>i) <code class='latex inline'>y = 5x - 2</code> </li> <li>ii) <code class='latex inline'>y =x^2 - 6x + 4</code> </li> <li>iii) <code class='latex inline'>y =x(x + 4)</code></li> <li>iv) <code class='latex inline'>y=2x^3 -4x^2 + 5x -1</code></li> </ul>
<p>Evaluate <code class='latex inline'>\displaystyle f(3) </code> for each of the following.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|} \hline x & 1 & 2 & 3 & 4 \\ \hline y & 2 & 3 & 4 & 5 \\ \hline \end{array} </code></p>
<p>Represent each set of data in a mapping diagram.</p><p><code class='latex inline'>\displaystyle \{(6,-7),(9,-7),(12,-7),(15,-7)\} </code></p>
<p>Represent each set of data in a mapping diagram.</p><p>a) <code class='latex inline'>\displaystyle \{(-4,18),(-3,14),(-2,10),(-1,6), </code>, <code class='latex inline'>\displaystyle (0,2),(1,-2)\} </code></p>
<p>State the domain and the range of each relation.</p><img src="/qimages/21839" />
<p>The mapping diagram below shows the relation between students and their marks on a math quiz.</p><p>a) Write the relation as a set of ordered pairs.</p><p>b) State the domain and range.</p><p>c) Is the relation a function? Explain.</p><img src="/qimages/77943" />
<p>In Exercises 19 and 20, find the value of <code class='latex inline'>\displaystyle x </code> so that <code class='latex inline'>\displaystyle f(x)=7 . </code></p><img src="/qimages/43355" />
<img src="/qimages/55108" />
<p>Find the domain and range of each relation and determine whether it is a function.</p><img src="/qimages/88572" />
<p>Identify the relation that is not a function.</p><img src="/qimages/7120" />
<p>The factors of <code class='latex inline'>4</code> are <code class='latex inline'>1, 2</code>, and <code class='latex inline'>4</code>. The sum of the factors is <code class='latex inline'>1 + 2+ 4 = 7</code>. The sum of the factors is called the sigma function. Therefore, <code class='latex inline'>f(4) = 7</code>.</p><p>a) What is <code class='latex inline'>f(12)</code>? Show your work.</p><p>b) Are there others that will work? Show your work.</p>
<p>Express each relation as a set of ordered pairs. Describe the domain and range.</p><img src="/qimages/38300" />
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(-2,3),(-1,3),(0,3),(1,4)\} </code></p>
<p>Determine whether each relation is a function, and state its domain and range.</p><img src="/qimages/7280" />
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77918" />
<p>Explain the meaning of <code class='latex inline'>\displaystyle f(3)=\frac{1}{2} </code></p>
<p>For each given domain and range, draw two relations on the same axes: one that is a function and one that is not a function.</p> <ul> <li>domain <code class='latex inline'>\{x\in \mathbb{R}\}</code></li> <li>range <code class='latex inline'>\{y\in \mathbb{R}, y \leq 3\}</code></li> </ul>
<p>If <code class='latex inline'>\displaystyle g(x)=3 x-1 </code>, determine the following:</p><p><code class='latex inline'>\displaystyle \begin{array}{llll}\text { a. } g(2) & \text { b. } g(-3) & \text { c. } g\left(\frac{1}{3}\right) & \text { d. } g(a)\end{array} </code></p>
<p>Evaluate <code class='latex inline'>\displaystyle f(4) </code> for each of the following.</p><p> <code class='latex inline'>\displaystyle f=\{(1,5),(3,2),(4,1),(6,2)\} </code></p>
<p>Determine whether each relation is a function.</p><img src="/qimages/12331" />
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/38337" />
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/38341" />
<p>CHALLENGE Consider <code class='latex inline'>\displaystyle f(x)=-4.3 x-2 . </code> Write <code class='latex inline'>\displaystyle f(g+3.5) </code> and simplify by combining like terms.</p>
<p><code class='latex inline'>\displaystyle f(x)=6 x+7 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}-4 </code>, find each value.</p><p><code class='latex inline'>\displaystyle f(m) </code></p>
<p>Evaluate <code class='latex inline'>\displaystyle f(4) </code> for each of the following.</p><img src="/qimages/163371" />
<p>Evaluate <code class='latex inline'>\displaystyle f(4) </code> for each of the following.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|r|r|r|r|} \hline x & 2 & 4 & 6 & 8 \\ \hline f(x) & 4 & 8 & 12 & 16 \\ \hline \end{array} </code></p>
<p>Evaluate each function.</p><p><code class='latex inline'>\displaystyle f(2.5) </code> if <code class='latex inline'>\displaystyle f(x)=16 x^{2} </code></p>
<p>Determine whether each relation is a function. Assume that each different variable has a different value.</p><p><code class='latex inline'>\displaystyle \{(a, b),(b, c),(c, d),(d, e)\} </code></p>
<p>The relation that is also a function is</p><p>A. <code class='latex inline'>x^2 + y^2 = 25</code></p><p>B. <code class='latex inline'>y^2 =x</code></p><p>C. <code class='latex inline'>x^2 =y</code></p><p>D. <code class='latex inline'>x^2 - y^2 = 25</code></p>
<p>Determine whether each relation is a function.</p><img src="/qimages/24658" />
<p>Find each value if <code class='latex inline'>\displaystyle f(x)=3 x+2, g(x)=-2 x^{2} </code>, and <code class='latex inline'>\displaystyle h(x)=-4 x^{2}-2 x+5 </code></p><p><code class='latex inline'>\displaystyle f\left(\frac{2}{3}\right) </code></p>
<p>Which relations are functions? Explain. For each graph, state the domain and range.</p><img src="/qimages/77937" />
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77922" />
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77925" />
<p>Find each value if <code class='latex inline'>\displaystyle f(x)=3 x+2, g(x)=-2 x^{2} </code>, and <code class='latex inline'>\displaystyle h(x)=-4 x^{2}-2 x+5 </code></p><p><code class='latex inline'>\displaystyle g(-6) </code></p>
<p>Consider the relation <code class='latex inline'>f: x^2 + y^2 = 25</code> and <code class='latex inline'>g: y = \sqrt{25- x^2}</code>. Determine whether each relation is a function. State the domain and range of each relation. Show your work.</p>
<p>Which of the following explains why a relation that fails the vertical line test is not a function?</p>
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77923" />
<p>Determine whether the graph represents a function. Explain. </p><img src="/qimages/43230" />
<p>Determine whether each relation is a function. Assume that each different variable has a different value.</p><p><code class='latex inline'>\displaystyle \{(c, e),(c, d),(c, b)\} </code></p>
<p>Describe the graph of relation that satisfies each set of conditions.</p><p>There are two entries in the domain and five entries in the range.</p>
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/12958" />
<p>Does the table or graph represent a linear or nonlinear function? Explain.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|c|c|c|c|} \hline \boldsymbol{x} & 2 & 7 & 12 & 17 \\ \hline \boldsymbol{y} & 2 & -1 & -4 & -7 \\ \hline \end{array} </code></p>
<p>State the domain and the range of each relation.</p><img src="/qimages/21837" />
<p>Represent each set of data in a mapping diagram.</p><p>b) <code class='latex inline'>\displaystyle \{(-3,3),(-2,-3),(-1,3),(-1,-3), </code>, <code class='latex inline'>\displaystyle (-2,3),(-3,-3)\} </code></p>
<p>Determine whether the relation is a function, and state its domain and range. Show your work.</p><p><code class='latex inline'>x^2 = 2y + 1</code></p>
<p>Is the relation a function? Why or why not?</p><p><code class='latex inline'>\displaystyle \begin{aligned} k:(x, y) &=(\text { number of households, number of TV's }) \\ &=\{(1,5),(1,4),(2,3),(3,2)\} \end{aligned} </code></p>
<p>Determine whether each relation is a function. Explain.</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline Domain & Range \\ \hline 4 & 6 \\ \hline-5 & 3 \\ \hline 6 & -3 \\ \hline-5 & 5 \\ \hline\end{array} </code></p>
<p>State which of the following are graphs of functions.</p><img src="/qimages/63850" />
<p>Determine the domain and range of each of the following relations.</p><img src="/qimages/63864" />
<p>If <code class='latex inline'>\displaystyle f(x)=-2 x-3 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}+5 x </code>, find each value.</p><p><code class='latex inline'>\displaystyle f(r+2) </code></p>
<p>List the domain and range ofeach relation.</p><p><code class='latex inline'>\displaystyle \{(0,4),(4,0),(-3,-4),(-4,-3)\} </code></p>
<p>If <code class='latex inline'>\displaystyle f(3 b-1)=9 b-1 </code>, find one possible expression for <code class='latex inline'>\displaystyle f(x) </code>.</p>
<p>Is each relation a function? If not, which ordered pair should be removed to make the relation a function?</p><img src="/qimages/77933" />
<p>Every year, the Rock and Roll Hall of Fame and Museum inducts legendary musicians and musical acts to the Hall. The table shows the number of inductees for each year.</p><p>Represent the data using each of the following:</p><p>a. a mapping diagram</p><p>b. ordered pairs</p><p>c. a graph on the coordinate plane</p><p>Rock and Roll Hall of Fame Inductees <code class='latex inline'>\displaystyle \begin{array}{c|c|c|c} Year & Number of Inductees & Year & Number of Inductees \\ \hline 2001 & 11 & 2004 & 8 \\ 2002 & 8 & 2005 & 7 \\ 2003 & 9 & 2006 & 6 \\ \hline \end{array} </code></p>
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77919" />
<p>Bill called a garage to ask for a price quote on the size and type of tire he needed.</p><p>a) Explain why this scenario represents a function.</p><p>b) If Bill had given the clerk the tire price, would the clerk be able to tell Bill the tire size and type? Would this scenario represent a function?</p>
<p>State the domain and range of each relation. Then determine whether the relation is a function, and justify your answer.</p><p><code class='latex inline'>\{(1, 4), (1, 9), (2, 7), (,3 -5), (4, 11)\}</code></p>
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(0,2),(1,5)(3,11),(4,14),(5,15)\} </code></p>
<p>Determine whether each relation is a function. Assume that each different variable has a different value.</p><p><code class='latex inline'>\displaystyle \{(b, b),(c, d),(d, c),(c, a)\} </code></p>
<p>Determine whether each relation is a function.</p><p><code class='latex inline'>\displaystyle \{(1,1),(2,0),(3,1),(4,3),(0,2)\} </code></p>
<p>The table below lists all the ordered pairs that belong to the function <code class='latex inline'>g(x)</code></p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|c|c|c|c|} \hline \mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \mathrm{g}(\mathrm{x}) & 3 & 4 & 7 & 12 & 19 & 28 \\ \hline \end{array} </code></p><p><strong>(a)</strong> Determine an equation for <code class='latex inline'>g(x)</code>.</p><p><strong>(b)</strong> Does <code class='latex inline'>g(3) - g(2) = g(3- 2)</code>? Explain.</p>
<p>The graph of <code class='latex inline'>\displaystyle y=f(x) </code> is shown at the right.</p><p>a) State the domain and range of <code class='latex inline'>\displaystyle f </code>.</p><p>b) Evaluate.</p><p>i) <code class='latex inline'>\displaystyle f(3) </code></p><p>ii) <code class='latex inline'>\displaystyle f(5) </code></p><p>iii) <code class='latex inline'>\displaystyle f(5-3) </code></p><p>iv) <code class='latex inline'>\displaystyle f(5)-f(3) </code></p><p>c) In part (b), why is the value in (iv) not the same as that in (iii)?</p><p>d) <code class='latex inline'>\displaystyle f(2)=5 . </code> What is the corresponding ordered pair? What does 2 represent? What does <code class='latex inline'>\displaystyle f(2) </code> represent?</p><img src="/qimages/163366" />
<p>State which of the following are graphs of functions.</p><img src="/qimages/63851" />
<p>Evaluate each function.</p><p><code class='latex inline'>\displaystyle f(-8) </code> if <code class='latex inline'>\displaystyle f(x)=5 x^{3}+1 </code></p>
<p>Determine whether each relation is a function.</p><p><code class='latex inline'>\displaystyle x=15 </code></p>
<p>Express each relation as a table, a graph, and a mapping. Then determine the domain and range.</p><p><code class='latex inline'>\displaystyle \{(5,2),(5,6),(3,-2),(0,-2)\} </code></p>
<p>Which variable would be associated with the domain for the following pairs of related quantities? Which variable would be associated with the range? Explain.</p><p>a) heating bill, outdoor temperature</p><p>b) report card mark, time spent doing homework</p><p>c) person, date of birth</p><p>d) number of slices of pizza, number of cuts</p>
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(-3,4),(2,1),(4,4),(9,5)\} </code></p>
<p>Evaluate each function for the given value of <code class='latex inline'>\displaystyle x </code>, and write the input <code class='latex inline'>\displaystyle x </code> and output <code class='latex inline'>\displaystyle f(x) </code> as an ordered pair.</p><p><code class='latex inline'>\displaystyle f(x)=\frac{2}{9} x-\frac{9}{2} </code> for <code class='latex inline'>\displaystyle x=9 </code></p>
<p>In Exercises 19 and 20, find the value of <code class='latex inline'>\displaystyle x </code> so that <code class='latex inline'>\displaystyle f(x)=7 . </code></p><img src="/qimages/43356" />
<p>Evaluate <code class='latex inline'>\displaystyle f(3) </code> for each of the following.</p><img src="/qimages/163357" />
<p>Determine the domain and range of each of the following relations.</p><img src="/qimages/63861" />
<p>Which is different? Find &quot;both&quot; answers.</p> <ul> <li>Find the range of the function represented by the table.</li> <li><p>Find the inputs of the function represented by the table.</p></li> <li><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|c|} \hline \boldsymbol{x} & -1 & 0 & 1 \\ \hline \boldsymbol{y} & 7 & 5 & -1 \\ \hline \end{array} </code></p></li> <li><p>Find the <code class='latex inline'>\displaystyle x </code> -values of the function represented by <code class='latex inline'>\displaystyle (-1,7),(0,5) </code>, and <code class='latex inline'>\displaystyle (1,-1) </code>.</p></li> <li><p>Find the domain of the function represented by <code class='latex inline'>\displaystyle (-1,7),(0,5) </code>, and <code class='latex inline'>\displaystyle (1,-1) </code>.</p></li> </ul>
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77917" />
<p>If <code class='latex inline'>f(x)=20-2x</code>, find <code class='latex inline'>f(7)</code>.</p><p>A. 6</p><p>B. 7</p><p>C. 13</p><p>D. 14</p>
<p>Find the domain and range of each relation, and determine whether it is a function.</p><img src="/qimages/88487" />
<p>The factors of <code class='latex inline'>4</code> are <code class='latex inline'>1, 2</code>, and <code class='latex inline'>4</code>. The sum of the factors is <code class='latex inline'>1 + 2+ 4 = 7</code>. The sum of the factors is called the sigma function. Therefore, <code class='latex inline'>f(4) = 7</code>.</p><p>What is <code class='latex inline'>f(15)</code>? Show your work.</p>
<p>State the domain and range of the relation. Then determine whether the relation is a function, and justify your answer.</p><p><code class='latex inline'> \displaystyle y=\frac{1}{x + 3} </code></p>
<p><code class='latex inline'>\displaystyle f(x)=6 x+7 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}-4 </code>, find each value.</p><p><code class='latex inline'>\displaystyle g(5) </code></p>
<p>Represent each set of data in a mapping diagram.</p><p>c) <code class='latex inline'>\displaystyle \{(2,1),(3,3),(4,5),(5,1),(6,3),(7,5)\} </code></p>
<p>Determine the domain and range of each of the following relations.</p><img src="/qimages/63862" />
<p>Use the vertical line test to determine whether the relation is a function.</p><img src="/qimages/55069" />
<p>Graph the relation <code class='latex inline'>\displaystyle \{(-2,1),(0,2),(-1,-1),(-2,-2)\} . </code> What are the domain and range?</p>
<p>Is the relation a function? Why or why not?</p><img src="/qimages/77929" />
<p>A rock rolls off a cliff <code class='latex inline'>\displaystyle 66 \mathrm{~m} </code> high. Which set of values best represents the range in the relationship between the time elapsed, in seconds, and the resultant height, in metres? Explain.</p><p>a) 100 to 200</p><p>c) <code class='latex inline'>\displaystyle -100 </code> to 100</p><p>b) <code class='latex inline'>\displaystyle -100 </code> to 0</p><p>d) 0 to 66</p>
<p><code class='latex inline'>\displaystyle f(x)=6 x+7 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}-4 </code>, find each value.</p><p><code class='latex inline'>\displaystyle g(-4 t) </code></p>
<p>Find each value if <code class='latex inline'>\displaystyle f(x)=3 x+2, g(x)=-2 x^{2} </code>, and <code class='latex inline'>\displaystyle h(x)=-4 x^{2}-2 x+5 </code></p><p><code class='latex inline'>\displaystyle h(3) </code></p>
<p>Which scatter plot represents a function? Explain. For each graph, state the domain and range.</p><img src="/qimages/77935" />
<p>Determine whether each relation is a function, and state its domain and range.</p><p><code class='latex inline'>\{(2, 7), (1, 3), (2, 6), (10, -1)\}</code></p>
<p>Is each relation a function? If not, which ordered pair should be removed to make the relation a function?</p><img src="/qimages/77932" />
<p>For each given domain and range, draw two relations on the same axes: one that is a function and one that is not a function.</p> <ul> <li>domain <code class='latex inline'>\{x\in \mathbb{R}, x \leq 5\}</code></li> <li>range <code class='latex inline'>\{y\in \mathbb{R}, y \geq - 6\}</code></li> </ul>
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/12965" />
<p>If <code class='latex inline'>\displaystyle f(x)=7-3 x </code> and <code class='latex inline'>\displaystyle g(x)=3 x-7 </code>, what is the value of <code class='latex inline'>\displaystyle f(1)+g(1) </code> ?</p>
<p>Use the vertical line test to determine whether the relation is a function.</p><img src="/qimages/55067" />
<img src="/qimages/55060" />
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(-3,2),(-1,4),(1,4),(3,2),(5,3)\} </code></p>
<p>CCSS SENSE-MAKING Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the <code class='latex inline'>\displaystyle x </code> -coordinate of any relative extrema, and the end behavior of the graph.</p><img src="/qimages/38410" />
<p>State the domain and the range of each relation.</p><img src="/qimages/21838" />
<p>Determine whether each relation is a function. Assume that each different variable has a different value.</p><p><code class='latex inline'>\displaystyle \{(a, b),(b, a),(c, c),(e, d)\} </code></p>
<p>Martin wants to build an additional closet in a corner of his bedroom. Because the closet will be in a corner, only two new walls need to be built. The total length of the two new walls must be <code class='latex inline'>12</code> m. Martin wants the length of the closet to be twice as long as the width, as shown in the diagram. </p><p>What is <code class='latex inline'>l</code> as a function of <code class='latex inline'>w</code>? Show your work.</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>d) <code class='latex inline'>\displaystyle f(x)=7 </code></p>
<p>Express each relation as a table, a graph, and a mapping. Then determine the domain and range.</p><p><code class='latex inline'>\displaystyle \{(5,-7),(-1,4),(0,-5),(-2,3)\} </code></p>
<p>Determine whether the relation is a function. Explain.</p><img src="/qimages/44298" />
<p>Determine whether each relation is a function.</p><p><code class='latex inline'>\displaystyle y=3 x+2 y </code></p>
<p>If <code class='latex inline'>f(x)=3x-2</code> and <code class='latex inline'>g(x)=x^2-5</code>, find each value.</p><p><code class='latex inline'>g(-3)</code></p>
<p>Determine whether each relation is a function.</p><img src="/qimages/24657" />
<p>CCSS SENSE-MAKING Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the <code class='latex inline'>\displaystyle x </code> -coordinate of any relative extrema, and the end behavior of the graph.</p><img src="/qimages/38403" />
<p>Dates and outdoor temperatures are related. The hottest temperature recorded in Canada was <code class='latex inline'>\displaystyle 45^{\circ} \mathrm{C} </code> at Midvale and Yellow Grass, Saskatchewan, on July <code class='latex inline'>\displaystyle 5,1937 . </code> The coldest temperature recorded in Canada was <code class='latex inline'>\displaystyle -63^{\circ} \mathrm{C} </code>, in Snag, in the Yukon Territories, on February 3, <code class='latex inline'>\displaystyle 1947 . </code></p><p>a) What is the independent variable in this relation? What is the dependent variable?</p><p>b) What is the domain?</p><p>c) What is the range?</p><p>d) Is one variable a function of the other? Explain.</p>
<p>Use words and function notation to describe the transformation that can be applied to each 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 <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code>.</p><img src="/qimages/5231" />
<p>a) Express <code class='latex inline'>g: x \to \frac{-2}{x+3}</code> and </p><p><code class='latex inline'>\displaystyle h: x \to 4x^2 -5x </code> in functino nottation.</p><p>b) Determine</p> <ul> <li>i) <code class='latex inline'>h(-1) + h(1)</code></li> <li>ii) <code class='latex inline'>4g(1) -h(2)</code></li> <li>iii) <code class='latex inline'>\sqrt{h(-1)}</code></li> <li>iv) <code class='latex inline'>7[g(-5)]^2</code></li> </ul>
<p>Consider the graph of <code class='latex inline'>y = \sqrt{25 -x^2}</code></p><img src="/qimages/21742" /><p>Use transformations to sketch each graph of <code class='latex inline'>g(x)</code>. Write the equation of <code class='latex inline'>g(x)</code> and state the domain and range.</p><p>a) <code class='latex inline'>g(x) = 2f(x)</code></p><p>b) <code class='latex inline'>g(x) = f(2x)</code></p><p>c) <code class='latex inline'>g(x) = \frac{1}{2}f(x)</code></p><p>d) <code class='latex inline'>g(x) = f(\frac{1}{2}x)</code></p>
<p>Find <code class='latex inline'>\displaystyle f(3) </code> for each function. Sketch a graph of each function.</p><p><code class='latex inline'>\displaystyle f(x)=2(x-3)(x+1) </code></p>
<p>Use the vertical line test to determine whether the relation is a function.</p><img src="/qimages/55070" />
<ol> <li>Communication a) Is the set of ordered pairs <code class='latex inline'>\displaystyle (n, f) </code> a function, if <code class='latex inline'>\displaystyle n </code> is a person&#39;s name and <code class='latex inline'>\displaystyle f </code> is the person&#39;s fingerprints? b) Reverse the terms of the ordered pairs so that the set of ordered pairs is <code class='latex inline'>\displaystyle (f, n) </code>. Is the new set of ordered pairs a function? Explain.</li> </ol>
<p>Given <code class='latex inline'>f(x) = x^2 -5x + 3</code>, then</p><p>A. f(-1) = -3</p><p>B. f(-1) = 7</p><p>C. f(-1) = -1</p><p>D. f(-1) = 9</p>
<p>Determine the function that describe the following function rules. Show your work.</p> <ul> <li>The input is 3 less than the output.</li> </ul>
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77920" />
<p>A function has the following domain and range:</p><p><code class='latex inline'>\displaystyle \begin{aligned} \text { Domain } &=\{t \in \mathbf{R} \mid-3 \leq t \leq 5\} \\\\ \text { Range } &=\{g(t) \in \mathbf{R} \mid 0 \leq g(t) \leq 10\} \end{aligned} </code></p><p>Draw a sketch of this function if it is quadratic.</p>
<p>Determine the function that describe the following function rules. Show your work.</p> <ul> <li>The output is 5 less than the input multiplied by 2.</li> </ul>
<p>State the domain and range of each relation.</p><p><code class='latex inline'>\displaystyle \{(3,1),(4,-2),(5,3),(6,0)\} </code></p>
<p>Determine whether each relation is a function.</p><p><code class='latex inline'>\displaystyle \{(4,5),(3,-2),(-2,5),(4,7)\} </code></p>
<p><code class='latex inline'>\displaystyle f(x)=6 x+7 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}-4 </code>, find each value.</p><p><code class='latex inline'>\displaystyle f(2)+g(2) </code></p>
<p>Is the relation a function? Why or why not?</p><p><code class='latex inline'>\displaystyle \begin{aligned} h:(x, y) &=(\text { age of child, number of siblings }) \\ &=\{(1,4),(2,4),(3,3),(4,2)\} \end{aligned} </code></p>
<p>Determine which of the following relations is a function.</p><p>F <code class='latex inline'>\displaystyle \{(-3,2),(4,1),(-3,5)\} </code> G <code class='latex inline'>\displaystyle \{(2,-1),(4,-1),(2,6)\} </code> H <code class='latex inline'>\displaystyle \{(-3,-4),(-3,6),(8,-2)\} </code> J <code class='latex inline'>\displaystyle \{(5,-1),(3,-2),(-2,-2)\} </code></p>
<p>Determine the equations that describe the following function rules. Show your work.</p> <ul> <li>Subtract 2 from the input and then multiply by 3 to find the output.</li> </ul>
<p>The table gives typical resting pulse rates for six different mammals.</p><img src="/qimages/77941" /><p>a) Is the resting pulse rate a function of the type of mammal? Explain</p><p>b) If more mammals and their resting pulse rates were included, would the extended table of values be a function? Explain.</p>
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/12963" />
<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 = 4x + 3</code></p>
<p>Find the domain and range of each relation, and determine whether it is a function.</p><img src="/qimages/88488" />
<p>Determine the domain and range of each of the following relations.</p><img src="/qimages/63863" />
<p>Determine whether each relation is a function. Explain.</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|}\hline Domain & Ralige \\ \hline 2 & 6 \\ \hline 5 & 7 \\ \hline 6 & 9 \\ \hline 6 & 10 \\ \hline\end{array} </code></p>
<p>Find <code class='latex inline'>\displaystyle f(3) </code> for each function. Sketch a graph of each function.</p><p><code class='latex inline'>\displaystyle f(x)=-1 </code></p>
<p>Find each value if <code class='latex inline'>\displaystyle f(x)=3 x+2, g(x)=-2 x^{2} </code>, and <code class='latex inline'>\displaystyle h(x)=-4 x^{2}-2 x+5 </code></p><p><code class='latex inline'>\displaystyle f(9) </code></p>
<p>Find <code class='latex inline'>\displaystyle f(3) </code> for each function. Sketch a graph of each function.</p><p> <code class='latex inline'>\displaystyle f(x)=7 x-5 </code></p>
<p>For each relation, state</p><p>i) the domain and the range</p><p>ii) whether or not it is a function, and justify your answer</p><img src="/qimages/77924" />
<p>Determine whether each relation is a function.</p><img src="/qimages/38366" />
<p>For each given domain and range, draw two relations on the same axes: one that is a function and one that is not a function.</p> <ul> <li>domain <code class='latex inline'>\{x\in \mathbb{R}, x \geq - 4\}</code></li> <li>range <code class='latex inline'>\{y\in \mathbb{R}, y \geq 1\}</code></li> </ul>
<p>The factors of <code class='latex inline'>4</code> are <code class='latex inline'>1, 2</code>, and <code class='latex inline'>4</code>. The sum of the factors is <code class='latex inline'>1 + 2+ 4 = 7</code>. The sum of the factors is called the sigma function. Therefore, <code class='latex inline'>f(4) = 7</code>.</p><p>Find <code class='latex inline'>f(6), f(7)</code>, and <code class='latex inline'>f(8)</code>. Show your work.</p>
<p>Determine whether each relation is a function.</p><img src="/qimages/24659" />
<p>If <code class='latex inline'>f(x)=3x-2</code> and <code class='latex inline'>g(x)=x^2-5</code>, find each value.</p><p><code class='latex inline'>f(4)</code></p>
<p>Describe the graph of relation that satisfies the set of conditions below.</p><p>Three are three entries in the domain and three entries in the range.</p>
<p>If <code class='latex inline'>\displaystyle f(x)=-2 x-3 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}+5 x </code>, find each value.</p><p><code class='latex inline'>\displaystyle f(6) </code></p>
<p>Determine whether each relation is a function. Explain.</p><img src="/qimages/12962" />
<p>If <code class='latex inline'>\displaystyle f(x)=-2 x-3 </code> and <code class='latex inline'>\displaystyle g(x)=x^{2}+5 x </code>, find each value.</p><p><code class='latex inline'>\displaystyle f(0)-7 </code></p>
<p>State the domain and range of each relation, and state whether it is a function.</p><p><code class='latex inline'>\displaystyle \begin{array}{|r|r|}\hlinex & y \\ \hline 2 & 5 \\ 1 & 2 \\ 0 & 1 \\ -1 & 2 \\ -2 & 5 \\ \hline\end{array} </code></p>
<p>Reasoning A function consists of the pairs <code class='latex inline'>\displaystyle (2,3),(x, 4) </code>, and <code class='latex inline'>\displaystyle (5,6) . </code> What values, if any, may <code class='latex inline'>\displaystyle x </code> not assume?</p>
<p>For each of the following, determine <code class='latex inline'>\displaystyle f(3) </code></p><p>a) <code class='latex inline'>\displaystyle f=\{(1,2),(2,3),(3,5),(4,5)\} </code></p><p>b)<code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|} \hline \boldsymbol{x} & 1 & 3 & 5 & 7 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & 2 & 4 & 6 & 8 \\ \hline \end{array} </code>c) <code class='latex inline'>\displaystyle f(x)=4 x^{2}-2 x+1 </code></p><img src="/qimages/160128" /><p>d)</p>
<ol> <li>State the domain and the range for each relation. Determine if each relation is a function.</li> </ol> <img src="/qimages/17790" />
<p>For the given domain and range, draw one relation that is a function and one that is not. Use the same set of axes.</p><p>domain <code class='latex inline'>\displaystyle \{x \in \mathbb{R}, x \geq-4\} </code> range <code class='latex inline'>\displaystyle \{y \in \mathbb{R}, y \geq 1\} </code></p>
<p>Given the function <code class='latex inline'>\displaystyle f </code> represented by the given set of ordered pairs <code class='latex inline'>\displaystyle f=\{(-1,3),(0,4),(1,5),(2,6)\} </code>, determine <code class='latex inline'>\displaystyle f(0) </code> and <code class='latex inline'>\displaystyle f(2) </code></p>
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