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Similar Question 1
<p>If f(x) is a linear function with positive or negative slope, what will the domain and range of this function be?</p>
Similar Question 2
<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>a) <code class='latex inline'>\displaystyle f(x)=-\frac{3}{5} x+2 </code></p>
Similar Question 3
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>-0.1</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'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>1</code></p>
<p>Which of the Following statements is not true?</p><p>a) The horizontal line test can be used to show that a relation is a function.</p><p>b) The set of all possible input values of a function is called the domain.</p><p>c) he equation <code class='latex inline'>y = 3x + 5</code> describes a function.</p><p>d) This set of ordered pairs describes a function:</p><p><code class='latex inline'>\{(0, 1), (1, 2), (3, -3), (4, -1)\}</code></p>
<p>For <code class='latex inline'>g(t)=3t-2</code>, determine each value.</p><p><code class='latex inline'> \displaystyle g(13) </code></p>
<p>Does the table or graph represent a linear or nonlinear function? Explain.</p><img src="/qimages/44302" />
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>0</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>a) <code class='latex inline'>\displaystyle f(x)=-\frac{3}{5} x+2 </code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>y=2x+3</code> for x ={-3, -2, -1, 1, 2, 3}</p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>0.5</code></p>
<p>ccsS REASONING The cost of sending cell phone pictures is given by <code class='latex inline'>\displaystyle y=0.25 x </code>, where <code class='latex inline'>\displaystyle x </code> is the number of pictures that you send and <code class='latex inline'>\displaystyle y </code> is the cost in dollars.</p><p>a. Write the equation in function notation. Interpret the function in terms of the context.</p><p>b. Find <code class='latex inline'>\displaystyle f(5) </code> and <code class='latex inline'>\displaystyle f(12) </code>. What do these values represent?</p><p>c. Determine the domain and range of this function.</p>
<p>A linear function machine uses a function of the form <code class='latex inline'>\displaystyle f(x)=a x+2 . </code> In each case, suppose the given point is on the function. Find the value of <code class='latex inline'>\displaystyle a </code>, and then write the defining equation.</p><p>b) <code class='latex inline'>\displaystyle (1,8) </code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>7</code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>100</code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>2</code></p>
<p>For each function, determine the range for the domain <code class='latex inline'>\{-2, -1, 0, 1, 2\}</code>.</p><p><code class='latex inline'>y = 8</code></p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>0</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|}\hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 3 & 1 \\ \hline 3 & -2 \\ 2 & 0 \\ 1 & -1 \\ 0 & -2 \\ \hline\end{array} </code></p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>0.5</code></p>
<p>If f(x) is a linear function with positive or negative slope, what will the domain and range of this function be?</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/77896" />
<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)=-9 x-2 </code> for <code class='latex inline'>\displaystyle x=7 </code></p>
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24673" />
<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) = 2f(x)</code></p><img src="/qimages/24524" />
<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'>b(x) = f(x + 2)</code></p>
<p>Plot the set of points on a grid. Describe the pattern and plot the next three points.</p> <ul> <li>P(1, 6), Q(-4, 4), R(-9, 2)</li> </ul>
<p>Solve each equation for the given domain. Graph the solution set.</p><p>The domain for <code class='latex inline'>3x+y=8</code> is {-􏰸1,2,5,8}. Find the range.</p>
<p>EDUCATION The average national math test scores <code class='latex inline'>\displaystyle f(t) </code> for 17 -year-olds can be represented as a function of the national science scores <code class='latex inline'>\displaystyle t </code> by <code class='latex inline'>\displaystyle f(t)=0.8 t+72 </code>.</p><p>a. Graph this function. Interpret the function in terms of the context.</p><p>b. What is the science score that corresponds to a math score of <code class='latex inline'>\displaystyle 308 ? </code></p><p>c. What is the domain and range of this function?</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/77894" />
<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>Find the value of each function at <code class='latex inline'>\displaystyle x=0 . </code> Sketch the graph of each function.</p><p>b) <code class='latex inline'>\displaystyle k(x)=5 x </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{12 x}{5} </code> for <code class='latex inline'>\displaystyle x=-1 </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>c) <code class='latex inline'>\displaystyle p(x)=-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><p><code class='latex inline'>y = 3x -5</code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>-4</code></p>
<p>Find the domain and range of each function. Explain your answers. <code class='latex inline'>\displaystyle f(x)=3 x-4 </code></p>
<p>Write each function in mapping notation.</p><p>a) <code class='latex inline'>\displaystyle f(x)=-7 x+1 </code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>-2</code></p>
<p>Consider the function <code class='latex inline'>\displaystyle g(t)=3 t+5 </code></p><p>a) Determine</p> <ul> <li><p>i) <code class='latex inline'>\displaystyle g(0) </code></p></li> <li><p>iii) <code class='latex inline'>\displaystyle g(2) </code></p></li> <li><p>v) <code class='latex inline'>\displaystyle g(1)-g(0) </code></p></li> <li><p>ii) <code class='latex inline'>\displaystyle g(1) </code></p></li> <li><p>iv) <code class='latex inline'>\displaystyle g(3) </code></p></li> <li><p>vi) <code class='latex inline'>\displaystyle g(2)-g(1) </code></p></li> </ul> <p>b) In part (a), what are the answers to (v) and (vi) commonly called?</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'>g</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/77898" />
<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'>m(x) = f(x) + 9</code></p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>4</code></p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>10</code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>1000</code></p>
<p>Write a linear function <code class='latex inline'>\displaystyle f </code> with the given values.</p><img src="/qimages/44400" /><img src="/qimages/152657" />
<p>Which equation does not belong with the other three? Explain your reasoning. </p><p><code class='latex inline'>\displaystyle y=-5 x-1; \quad 2 x-y=8; \quad y=x+4; \quad y=-3 x+13 </code></p>
<p>Plot the set of points on a grid. Describe the pattern and plot the next three points.</p> <ul> <li>G(3, 3), H(0, 0), I(-3, -3)</li> </ul>
<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 - 3) - 7</code></p>
<p>Find the domain and range of each function. Explain your answers. <code class='latex inline'>\displaystyle x=5 </code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>y=3x</code> for <code class='latex inline'>x=</code> {-3,-2, -1, 0, 1, 2, 3}</p>
<p>Consider linear relations that represent either horizontal lines, such as <code class='latex inline'>\displaystyle y=4 </code>, or vertical lines, such as <code class='latex inline'>\displaystyle x=6 </code>. What are the domain and range of these relations?</p>
<p>State the degree of each function, and identify which are linear and which are quadratic.</p><p><code class='latex inline'>\displaystyle 3 x-4 y=12 </code></p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>x= 3</code></p>
<p>If <code class='latex inline'>\displaystyle y=4 x-5 </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>-0.5</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 - 5) + 1</code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p>The range for <code class='latex inline'>2y-x=6</code> is {􏰸-4,􏰸-3,1,6,7}. Find the domain.</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>a) <code class='latex inline'>\displaystyle f(x)=3 x-1 </code></p>
<p>Evaluate the function for the given x-values.</p><p><code class='latex inline'>f(x) = 9x + 1; x = 0, 2</code></p>
<p>A linear function machine uses a function of the form <code class='latex inline'>\displaystyle f(x)=a x+2 . </code> In each case, suppose the given point is on the function. Find the value of <code class='latex inline'>\displaystyle a </code>, and then write the defining equation.</p><p>a) <code class='latex inline'>\displaystyle (4,-10) </code></p>
<p>Evaluate for the given x-values.</p><p><code class='latex inline'>\displaystyle f(x)=-2 x-3 ; x=-1, x=3 </code></p>
<p>Describe and correct the error in the statement about the domain.</p><img src="/qimages/43305" />
<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>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>5</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 + 4) + 6</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'>h(x) = f(x) - 5</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 + 2) - 8</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 + 18</code><br> <code class='latex inline'>g(x) = -f(-x)</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/77895" />
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>-0.1</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 x+1}{3} </code> for <code class='latex inline'>\displaystyle x=-5 </code></p>
<p>Solve each equation for the given domain. Graph the solution set.</p><p><code class='latex inline'>2y=x+2</code> for <code class='latex inline'>x=</code> {-4, -2, 0, 2, 4}</p>
<p>If <code class='latex inline'>\displaystyle y=8-2 x </code>, find the value of <code class='latex inline'>\displaystyle y </code> for each of the following values of <code class='latex inline'>\displaystyle x </code>.</p><p><code class='latex inline'>-3</code></p>
<p>Identify the intervals of increase/decrease, the symmetry, and the domain and rage of each function.</p><p><code class='latex inline'>\displaystyle f(x) = 3x </code></p>
<p>Write an equation in function notation for each relation.</p><img src="/qimages/24674" />
<p>Given <code class='latex inline'>\displaystyle f(x)=4 x+7 </code>, determine the value of <code class='latex inline'>\displaystyle x </code> if <code class='latex inline'>\displaystyle f(x)=15 </code>.</p>
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