Question 1

Give the equation of the vertical asymptote(s) of the rational function.
-$g(x)=\frac{x+5}{x^{2}+4 x-12}$

Accepted Answer

A)  $x=-6, x=2, y=0$ 
B)  $x=-6, x=2$ 
C)  $x=-5$ 
D)  $x=6, x=-2$ 
A)  $x=-6, x=2, y=0$ 
B)  $x=-6, x=2$ 
C)  $x=-5$ 
D)  $x=6, x=-2$

Question 2

Give the equation of the vertical asymptote(s) of the rational function.
-$g(x)=\frac{x-1}{x^{2}-4}$

Accepted Answer

A)  $x=2, x=-2$ 
B)  $x=-2$ 
C)  $x=1$ 
D)  $x=2$ 
A)  $x=2, x=-2$ 
B)  $x=-2$ 
C)  $x=1$ 
D)  $x=2$

Question 3

Use a graphing calculator to find a viewing window that shows a complete graph of the given polynomial function(that is, a graph that includes all the peaks and valleys and indicates how the curve moves away frem the $x$ axis at thefar left and far right.) There are many possible correct answers.
-$f(x)=x^{5}-2 x^{4}+2 x^{3}-7 x^{2}-8 x+3$

Accepted Answer

Answers wi

Question 4

Use a graphing calculator to find a viewing window that shows a complete graph of the given polynomial function(that is, a graph that includes all the peaks and valleys and indicates how the curve moves away frem the $x$ axis at thefar left and far right.) There are many possible correct answers.
-$f(x)=2 x^{4}-3 x^{3}-6 x^{2}-10 x+20$

Accepted Answer

Answers wi

Question 5

Match the function to the correct graph.
-$y=x^{3}-3 x+2$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Solve the problem.
-At a manufacturing plant, the total cost (in dollars) to produce $x$ items is
$C(x)=4.16 x+40,000$.
What is the total cost to produce 2900 items?

Accepted Answer

A)  $\$ 40,004.16$ 
B)  $\$ 53,564$ 
C)  $\$ 52,064$ 
D)  $\$ 12,064$ 
A)  $\$ 40,004.16$ 
B)  $\$ 53,564$ 
C)  $\$ 52,064$ 
D)  $\$ 12,064$

Question 7

Solve the problem.
-An open-top box is to be made by cutting small identical squares from each corner of a 12-by-12-in. sheet of tin and bending up the sides. If each corner square is $x$ inches on a side, the volume of the box (in in. ${ }^{3}$ ) is given by:
$$\mathrm{V}(\mathrm{x})=144 \mathrm{x}-48 \mathrm{x}^{2}+4 \mathrm{x}^{3}$$
By sketching the graph of $\mathrm{V}(\mathrm{x})$, estimate what values of $\mathrm{x}$ result in a box with a volume greater than $64 \mathrm{in}^{3}$.

Accepted Answer

A)  1.5 in. $\leq x \leq 2.5$ in. 
B)  0.1 in. $\leq x \leq 5.0$ in. 
C)  1.0 in. $\leq x \leq 3.0$ in. 
D)  0.54 in. $\leq x \leq 4$ in. 
A)  1.5 in. $\leq x \leq 2.5$ in. 
B)  0.1 in. $\leq x \leq 5.0$ in. 
C)  1.0 in. $\leq x \leq 3.0$ in. 
D)  0.54 in. $\leq x \leq 4$ in.

Question 8

Solve the problem.
-The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

Accepted Answer

A)  yes; 3,5 
B)  yes; 4 only 
C)  yes; 3 only 
D)  yes; 4,6 
A)  yes; 3,5 
B)  yes; 4 only 
C)  yes; 3 only 
D)  yes; 4,6

Question 9

State whether the parabola opens upward or downward.
-$f(x)=-x^{2}-5$

Accepted Answer

A)  Downward 
B)  Upward 
A)  Downward 
B)  Upward

Question 10

Graph the function.
-$f(x)= \begin{cases}-2 x & \text { if } x<-2 \ |x| & \text { if } x \geq-2\end{cases}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 11

Evaluate the function.
-Given that $f(x)=\frac{1}{4-3 x}$, find $f(r-3)$.

Accepted Answer

A)  $\frac{1}{r-3-3 x}$ 
B)  $\frac{1}{1-3 r}$ 
C)  $\frac{1}{13+3 b}$ 
D)  $\frac{1}{13-3 r}$ 
A)  $\frac{1}{r-3-3 x}$ 
B)  $\frac{1}{1-3 r}$ 
C)  $\frac{1}{13+3 b}$ 
D)  $\frac{1}{13-3 r}$

Question 12

Graph the function.
-$f(x)= \begin{cases}2 x & \text { if } x \leq-1 \ -|x| & \text { if } x>-1\end{cases}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Solve the problem.
-Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c=2 x^{2}-192 x+54$, where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Accepted Answer

A)  27 watches 
B)  54 watches 
C)  48 watches 
D)  20 watches 
A)  27 watches 
B)  54 watches 
C)  48 watches 
D)  20 watches

Question 14

Graph the function.
-$y=[x]+1$

Accepted Answer

A)    
B)    
A)    
B)

Question 15

Solve the problem.
-An oil refinery can produce gasoline, heating oil, or a combination of the two. The product exchange function for gasoline, $x$, and heating oil, $y$, in thousands of gallons per week is:
$$y=\frac{72,000-8 x}{36+2 x}$$
By sketching the quadrant I portion of the graph of this function, estimate the maximum quantity of each product that can be produced per week.

Accepted Answer

A)  gasoline: $9,000,000$ gal; heating oil: $2,000,000$ gal 
B)  gasoline: 2,000,000 gal; heating oil: $9,000,000$ gal 
C)  gasoline: 4,500,000 gal; heating oil: 1,000,000 gal 
D)  gasoline: 9000 gal; heating oil: 2000 gal 
A)  gasoline: $9,000,000$ gal; heating oil: $2,000,000$ gal 
B)  gasoline: 2,000,000 gal; heating oil: $9,000,000$ gal 
C)  gasoline: 4,500,000 gal; heating oil: 1,000,000 gal 
D)  gasoline: 9000 gal; heating oil: 2000 gal

Question 16

Graph the function.
-A roller blade rental store charges $\$ 5$ plus $\$ 2$ per hour or fraction of an hour. Graph the ordered pairs (hours, cost).

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Write the word or phrase that best completes each statement or answers the question.
-The table shows the winning time for the women's 200 -meter run at seven consecutive summer Olympic Games.
   
Let $\mathrm{x}=1$ correspond to 1960 and let $\mathrm{f}(\mathrm{x})$ be the winning time for the women's 200 -meter run at the Olympics in year $x$. Using the points $(1,24.0)$ and $(25,21.81)$, the following linear function is obtained to model the data: $f(x)=-0.09125 x+24.09125$. According to this model, will the winning time ever reach 10 seconds? If so, when? Do you think that it makes sense to use the model to make predictions for future years?

Accepted Answer

Yes, according to the model, the winning

Question 18

Use the vertical line test to determine if the graph is a graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 19

Evaluate the function.
-given that $f(x)=\sqrt{-3 x}$, find $f(-k)$.

Accepted Answer

A)  $\sqrt{-3 \mathrm{k}}$ 
B)  $\sqrt{\mathrm{kx}}$ 
C)  $\sqrt{3 \mathrm{k}}$ 
D)  $\sqrt{-k x}$ 
A)  $\sqrt{-3 \mathrm{k}}$ 
B)  $\sqrt{\mathrm{kx}}$ 
C)  $\sqrt{3 \mathrm{k}}$ 
D)  $\sqrt{-k x}$

Question 20

Solve the problem.
-Suppose a cost-benefit model is given by $y=\frac{7.6 x}{100-x}$, where $y$ is the cost in thousands of dollars for removing $x$ percent of a given pollutant. Find the cost of removing $30 \%$, to the nearest dollar.

Accepted Answer

A)  $\$ 428$ 
B)  $\$ 2280$ 
C)  $\$ 7600$ 
D)  $\$ 3257$ 
A)  $\$ 428$ 
B)  $\$ 2280$ 
C)  $\$ 7600$ 
D)  $\$ 3257$

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x+5}{x^{2}+4 x-12}$

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x-1}{x^{2}-4}$

Match the function to the correct graph. - $y=x^{3}-3 x+2$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=4.16 x+40,000$ . What is the total cost to produce 2900 items?

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

State whether the parabola opens upward or downward. - $f(x)=-x^{2}-5$

Graph the function. - $f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}$ $Graph the function. - f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}$

Evaluate the function. -Given that $f(x)=\frac{1}{4-3 x}$ , find $f(r-3)$ .

Graph the function. - $f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}$ $Graph the function. - f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}$

Solve the problem. -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c=2 x^{2}-192 x+54$ , where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Graph the function. - $y=[x]+1$

Graph the function. -A roller blade rental store charges $\$ 5$ plus $\$ 2$ per hour or fraction of an hour. Graph the ordered pairs (hours, cost). $Graph the function. -A roller blade rental store charges \$ 5 plus \$ 2 per hour or fraction of an hour. Graph the ordered pairs (hours, cost).$

Use the vertical line test to determine if the graph is a graph of a function. -

Evaluate the function. -given that $f(x)=\sqrt{-3 x}$ , find $f(-k)$ .

Solve the problem. -Suppose a cost-benefit model is given by $y=\frac{7.6 x}{100-x}$ , where $y$ is the cost in thousands of dollars for removing $x$ percent of a given pollutant. Find the cost of removing $30 \%$ , to the nearest dollar.

Algebra and Equations

Graphs, Lines, and Inequalities

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Exam 3: Functions and Graphs

Give the equation of the vertical asymptote(s) of the rational function. - g(x)=x+5x2+4x−12g(x)=\frac{x+5}{x^{2}+4 x-12}g(x)=x2+4x−12x+5​

Give the equation of the vertical asymptote(s) of the rational function. - g(x)=x−1x2−4g(x)=\frac{x-1}{x^{2}-4}g(x)=x2−4x−1​

Match the function to the correct graph. - y=x3−3x+2y=x^{3}-3 x+2y=x3−3x+2

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce xxx items is C(x)=4.16x+40,000C(x)=4.16 x+40,000C(x)=4.16x+40,000 . What is the total cost to produce 2900 items?

Solve the problem. -The graph of a function is given below. Tell whether the graph could possibly be the graph of a polynomial function. If it could be the graph of a polynomial function, tell which of the following are possible degrees for the polynomial function: 3, 4, 5, 6 .

State whether the parabola opens upward or downward. - f(x)=−x2−5f(x)=-x^{2}-5f(x)=−x2−5

Graph the function. - f(x)={−2x if x<−2∣x∣ if x≥−2f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}f(x)={−2x∣x∣​ if x<−2 if x≥−2​

Evaluate the function. -Given that f(x)=14−3xf(x)=\frac{1}{4-3 x}f(x)=4−3x1​ , find f(r−3)f(r-3)f(r−3) .

Graph the function. - f(x)={2x if x≤−1−∣x∣ if x>−1f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}f(x)={2x−∣x∣​ if x≤−1 if x>−1​

Solve the problem. -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c=2x2−192x+54c=2 x^{2}-192 x+54c=2x2−192x+54 , where ccc is cost and xxx is the number of watches repaired. How many watches must he repair to have the lowest cost?

Graph the function. - y=[x]+1y=[x]+1y=[x]+1

Graph the function. -A roller blade rental store charges $5\$ 5$5 plus $2\$ 2$2 per hour or fraction of an hour. Graph the ordered pairs (hours, cost).

Use the vertical line test to determine if the graph is a graph of a function. -

Evaluate the function. -given that f(x)=−3xf(x)=\sqrt{-3 x}f(x)=−3x​ , find f(−k)f(-k)f(−k) .

Solve the problem. -Suppose a cost-benefit model is given by y=7.6x100−xy=\frac{7.6 x}{100-x}y=100−x7.6x​ , where yyy is the cost in thousands of dollars for removing xxx percent of a given pollutant. Find the cost of removing 30%30 \%30% , to the nearest dollar.

Algebra and Equations

Graphs, Lines, and Inequalities

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Integral Calculus

Multivariate Calculus

Filters

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x+5}{x^{2}+4 x-12}$

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x-1}{x^{2}-4}$

Match the function to the correct graph. - $y=x^{3}-3 x+2$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=4.16 x+40,000$ . What is the total cost to produce 2900 items?

State whether the parabola opens upward or downward. - $f(x)=-x^{2}-5$

Graph the function. - $f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}$ $Graph the function. - f(x)= \begin{cases}-2 x & \text { if } x<-2 \\ |x| & \text { if } x \geq-2\end{cases}$

Evaluate the function. -Given that $f(x)=\frac{1}{4-3 x}$ , find $f(r-3)$ .

Graph the function. - $f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}$ $Graph the function. - f(x)= \begin{cases}2 x & \text { if } x \leq-1 \\ -|x| & \text { if } x>-1\end{cases}$

Solve the problem. -Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c=2 x^{2}-192 x+54$ , where $c$ is cost and $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

Graph the function. - $y=[x]+1$

Graph the function. -A roller blade rental store charges $\$ 5$ plus $\$ 2$ per hour or fraction of an hour. Graph the ordered pairs (hours, cost). $Graph the function. -A roller blade rental store charges \$ 5 plus \$ 2 per hour or fraction of an hour. Graph the ordered pairs (hours, cost).$

Evaluate the function. -given that $f(x)=\sqrt{-3 x}$ , find $f(-k)$ .

Solve the problem. -Suppose a cost-benefit model is given by $y=\frac{7.6 x}{100-x}$ , where $y$ is the cost in thousands of dollars for removing $x$ percent of a given pollutant. Find the cost of removing $30 \%$ , to the nearest dollar.