Question 1

Give the equation of the vertical asymptote(s) of the rational function.
-$g(x)=\frac{4}{3 x+5}$

Accepted Answer

A)  $x=-\frac{5}{3}$ 
B)  $x=\frac{5}{3}$ 
C)  $\mathrm{y}=-\frac{5}{3}$ 
D)  $x=-\frac{3}{5}$ 
A)  $x=-\frac{5}{3}$ 
B)  $x=\frac{5}{3}$ 
C)  $\mathrm{y}=-\frac{5}{3}$ 
D)  $x=-\frac{3}{5}$

Question 2

Solve the problem.
-Given the following revenue and cost functions, find the $x$-value that makes profit a maximum. (Recall that profit equals revenue minus cost.)
$$R(x)=58 x-2 x^{2} ; C(x)=24 x+92$$

Accepted Answer

A)  9.5 
B)  8.5 
C)  14.5 
D)  17 
A)  9.5 
B)  8.5 
C)  14.5 
D)  17

Question 3

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; 5,6 
B)  yes; 4,6 
C)  yes; 6 only 
D)  no 
A)  yes; 5,6 
B)  yes; 4,6 
C)  yes; 6 only 
D)  no

Question 4

Use a graphing calculator to construct a table of values for the given function.
-Use a graphing calculator to display a table showing the (approximate) values of the function $f(x)=x^{3}-5 x^{2}-5 x$ at $4.3,4.7,5.1,5.5,5.9,6.3$.

Accepted Answer

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

Question 5

Graph the rational function.
-$f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}$

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
$C(x)=2.3 x+2970$.
What is the total cost to produce 2560 items?

Accepted Answer

A)  $\$ 7608$ 
B)  $\$ 10,578$ 
C)  $\$ 8858$ 
D)  $\$ 11,458$ 
A)  $\$ 7608$ 
B)  $\$ 10,578$ 
C)  $\$ 8858$ 
D)  $\$ 11,458$

Question 7

Graph.
-$f(x)=5(x+2)^{2}+3$

Accepted Answer

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

Question 8

Solve the problem.
-John owns a hotdog stand. His profit is represented by the equation $P=-x^{2}+14 x+59$, with $P$ being profits and $x$ the number of hotdogs. What is the most he can earn?

Accepted Answer

A)  $\$ 150$ 
B)  $\$ 49$ 
C)  $\$ 87$ 
D)  $\$ 108$ 
A)  $\$ 150$ 
B)  $\$ 49$ 
C)  $\$ 87$ 
D)  $\$ 108$

Question 9

Use the graph to solve the problem.
-In one city, the temperature in Fahrenheit on a typical summer day can be approximated by the following function:
$f(x)= \begin{cases}53+3.8 t & \text { if } 0 \leq t \leq 7 \ 79.6 & \text { if } 7<t \leq 10 \ -5.4 t+133.6 & \text { if } 10<t \leq 15\end{cases}$
Here, $t$ represents the number of hours since 6 a.m. The graph of this function is shown below. At what time does it start to get cooler?

Accepted Answer

A)  At 10 a.m. 
B)  At 4 p.m. 
C)  At 1 p.m. 
D)  At 3 p.m. 
A)  At 10 a.m. 
B)  At 4 p.m. 
C)  At 1 p.m. 
D)  At 3 p.m.

Question 10

Solve the problem.
-A house was purchased for $\$ 80,000$. After 6 years the value of the house was $\$ 134,000$. Assume that the appreciation in value is given by a linear equation. Find the equation.

Accepted Answer

A)  $y=80,000+9000 x$ 
B)  $y=9000 x$ 
C)  $\mathrm{y}=134,000$ 
D)  $y=80,000+6 x$ 
A)  $y=80,000+9000 x$ 
B)  $y=9000 x$ 
C)  $\mathrm{y}=134,000$ 
D)  $y=80,000+6 x$

Question 11

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; 5 only 
C)  no 
D)  yes; 5,6 
A)  yes; 3,5 
B)  yes; 5 only 
C)  no 
D)  yes; 5,6

Question 12

Evaluate the function.
-Find $f(-1)$ when $f(x)=x^{2}-3 x-1$

Accepted Answer

A)  -1 
B)  3 
C)  5 
D)  -3 
A)  -1 
B)  3 
C)  5 
D)  -3

Question 13

State whether the parabola opens upward or downward.
-$f(x)=-3 x^{2}+7 x+4$

Accepted Answer

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

Question 14

Find the appropriate linear cost or revenue function.
-Find the cost function given the following information. Fixed cost: $\$ 230$; marginal cost per item: $\$ 37$

Accepted Answer

A)  $C(x)=230 x-37$ 
B)  $C(x)=230 x+37$ 
C)  $C(x)=37 x+230$ 
D)  $C(x)=37 x-230$ 
A)  $C(x)=230 x-37$ 
B)  $C(x)=230 x+37$ 
C)  $C(x)=37 x+230$ 
D)  $C(x)=37 x-230$

Question 15

Solve the problem.
-Bob owns a watch repair shop. He has found that the weekly cost (in dollars) of operating his shop is given by
$$c(x)=2 x^{2}-58 x+40$$
Where $x$ is the number of watches repaired. What is the cost of operating the shop if the number of watches repaired is 39 ?

Accepted Answer

A)  $\$ 3862$ 
B)  $\$ 780$ 
C)  $\$ 820$ 
D)  $\$ 3024$ 
A)  $\$ 3862$ 
B)  $\$ 780$ 
C)  $\$ 820$ 
D)  $\$ 3024$

Question 16

Solve the problem.
-A lumber yard has fixed costs of $\$ 1730.30$ a day and variable costs of $\$ 1.00$ per board - foot produced. The company gets $\$ 2.30$ per board-foot sold. How many board - feet must be produced daily to reach the break-even point?

Accepted Answer

A)  887 board-feet 
B)  1331 board-feet 
C)  524 board-feet 
D)  1730 board-feet 
A)  887 board-feet 
B)  1331 board-feet 
C)  524 board-feet 
D)  1730 board-feet

Question 17

Solve the problem.
-Find $f(-4)$ for
$$f(x)= \begin{cases}5 x & \text { if } x \leq-1 \ x-3 & \text { if } x>-1\end{cases}$$

Accepted Answer

A)  -7 
B)  20 
C)  -20 
D)  1 
A)  -7 
B)  20 
C)  -20 
D)  1

Question 18

Determine the vertex of the parabola.
-$y=(x+1)^{2}$

Accepted Answer

A)  $(0,-1)$ 
B)  $(-1,0)$ 
C)  $(1,0)$ 
D)  $(0,1)$ 
A)  $(0,-1)$ 
B)  $(-1,0)$ 
C)  $(1,0)$ 
D)  $(0,1)$

Question 19

Determine whether the following rule defines $y$ as a function of $x$.
-$x=|y-3|$

Accepted Answer

A) True 
 B)False

Question 20

For the given function, find $\frac{f(x+h)-f(x)}{h}$.
-$x^{2}+2$

Accepted Answer

A)  $2 x+h$ 
B)  $\frac{h+4}{h}$ 
C)  $2 x+h+4$ 
D)  1 
A)  $2 x+h$ 
B)  $\frac{h+4}{h}$ 
C)  $2 x+h+4$ 
D)  1

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{4}{3 x+5}$

Solve the problem. -Given the following revenue and cost functions, find the $x$ -value that makes profit a maximum. (Recall that profit equals revenue minus cost.) $R(x)=58 x-2 x^{2} ; C(x)=24 x+92$

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 .

Use a graphing calculator to construct a table of values for the given function. -Use a graphing calculator to display a table showing the (approximate) values of the function $f(x)=x^{3}-5 x^{2}-5 x$ at $4.3,4.7,5.1,5.5,5.9,6.3$ .

Graph the rational function. - $f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}$ $Graph the rational function. - f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=2.3 x+2970$ . What is the total cost to produce 2560 items?

Graph. - $f(x)=5(x+2)^{2}+3$ $Graph. - f(x)=5(x+2)^{2}+3$

Solve the problem. -John owns a hotdog stand. His profit is represented by the equation $P=-x^{2}+14 x+59$ , with $P$ being profits and $x$ the number of hotdogs. What is the most he can earn?

Solve the problem. -A house was purchased for $\$ 80,000$ . After 6 years the value of the house was $\$ 134,000$ . Assume that the appreciation in value is given by a linear equation. Find the equation.

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 .

Evaluate the function. -Find $f(-1)$ when $f(x)=x^{2}-3 x-1$

State whether the parabola opens upward or downward. - $f(x)=-3 x^{2}+7 x+4$

Find the appropriate linear cost or revenue function. -Find the cost function given the following information. Fixed cost: $\$ 230$ ; marginal cost per item: $\$ 37$

Solve the problem. -Bob owns a watch repair shop. He has found that the weekly cost (in dollars) of operating his shop is given by $c(x)=2 x^{2}-58 x+40$ Where $x$ is the number of watches repaired. What is the cost of operating the shop if the number of watches repaired is 39 ?

Solve the problem. -A lumber yard has fixed costs of $\$ 1730.30$ a day and variable costs of $\$ 1.00$ per board - foot produced. The company gets $\$ 2.30$ per board-foot sold. How many board - feet must be produced daily to reach the break-even point?

Solve the problem. -Find $f(-4)$ for $f(x)= \begin{cases}5 x & \text { if } x \leq-1 \\ x-3 & \text { if } x>-1\end{cases}$

Determine the vertex of the parabola. - $y=(x+1)^{2}$

Determine whether the following rule defines $y$ as a function of $x$ . - $x=|y-3|$

For the given function, find $\frac{f(x+h)-f(x)}{h}$ . - $x^{2}+2$

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)=43x+5g(x)=\frac{4}{3 x+5}g(x)=3x+54​

Solve the problem. -Given the following revenue and cost functions, find the xxx -value that makes profit a maximum. (Recall that profit equals revenue minus cost.) R(x)=58x−2x2;C(x)=24x+92R(x)=58 x-2 x^{2} ; C(x)=24 x+92R(x)=58x−2x2;C(x)=24x+92

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 .

Graph the rational function. - f(x)=(x+2)(x−3)(x−4)2f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}f(x)=(x−4)2(x+2)(x−3)​

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce xxx items is C(x)=2.3x+2970C(x)=2.3 x+2970C(x)=2.3x+2970 . What is the total cost to produce 2560 items?

Graph. - f(x)=5(x+2)2+3f(x)=5(x+2)^{2}+3f(x)=5(x+2)2+3

Solve the problem. -John owns a hotdog stand. His profit is represented by the equation P=−x2+14x+59P=-x^{2}+14 x+59P=−x2+14x+59 , with PPP being profits and xxx the number of hotdogs. What is the most he can earn?

Solve the problem. -A house was purchased for $80,000\$ 80,000$80,000 . After 6 years the value of the house was $134,000\$ 134,000$134,000 . Assume that the appreciation in value is given by a linear equation. Find the equation.

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 .

Evaluate the function. -Find f(−1)f(-1)f(−1) when f(x)=x2−3x−1f(x)=x^{2}-3 x-1f(x)=x2−3x−1

State whether the parabola opens upward or downward. - f(x)=−3x2+7x+4f(x)=-3 x^{2}+7 x+4f(x)=−3x2+7x+4

Find the appropriate linear cost or revenue function. -Find the cost function given the following information. Fixed cost: $230\$ 230$230 ; marginal cost per item: $37\$ 37$37

Solve the problem. -A lumber yard has fixed costs of $1730.30\$ 1730.30$1730.30 a day and variable costs of $1.00\$ 1.00$1.00 per board - foot produced. The company gets $2.30\$ 2.30$2.30 per board-foot sold. How many board - feet must be produced daily to reach the break-even point?

Solve the problem. -Find f(−4)f(-4)f(−4) for f(x)={5x if x≤−1x−3 if x>−1f(x)= \begin{cases}5 x & \text { if } x \leq-1 \\ x-3 & \text { if } x>-1\end{cases}f(x)={5xx−3​ if x≤−1 if x>−1​

Determine the vertex of the parabola. - y=(x+1)2y=(x+1)^{2}y=(x+1)2

Determine whether the following rule defines yyy as a function of xxx . - x=∣y−3∣x=|y-3|x=∣y−3∣

For the given function, find f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ . - x2+2x^{2}+2x2+2

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. - $g(x)=\frac{4}{3 x+5}$

Solve the problem. -Given the following revenue and cost functions, find the $x$ -value that makes profit a maximum. (Recall that profit equals revenue minus cost.) $R(x)=58 x-2 x^{2} ; C(x)=24 x+92$

Graph the rational function. - $f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}$ $Graph the rational function. - f(x)=\frac{(x+2)(x-3)}{(x-4)^{2}}$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=2.3 x+2970$ . What is the total cost to produce 2560 items?

Graph. - $f(x)=5(x+2)^{2}+3$ $Graph. - f(x)=5(x+2)^{2}+3$

Solve the problem. -John owns a hotdog stand. His profit is represented by the equation $P=-x^{2}+14 x+59$ , with $P$ being profits and $x$ the number of hotdogs. What is the most he can earn?

Solve the problem. -A house was purchased for $\$ 80,000$ . After 6 years the value of the house was $\$ 134,000$ . Assume that the appreciation in value is given by a linear equation. Find the equation.

Evaluate the function. -Find $f(-1)$ when $f(x)=x^{2}-3 x-1$

State whether the parabola opens upward or downward. - $f(x)=-3 x^{2}+7 x+4$

Find the appropriate linear cost or revenue function. -Find the cost function given the following information. Fixed cost: $\$ 230$ ; marginal cost per item: $\$ 37$

Solve the problem. -A lumber yard has fixed costs of $\$ 1730.30$ a day and variable costs of $\$ 1.00$ per board - foot produced. The company gets $\$ 2.30$ per board-foot sold. How many board - feet must be produced daily to reach the break-even point?

Solve the problem. -Find $f(-4)$ for $f(x)= \begin{cases}5 x & \text { if } x \leq-1 \\ x-3 & \text { if } x>-1\end{cases}$

Determine the vertex of the parabola. - $y=(x+1)^{2}$

Determine whether the following rule defines $y$ as a function of $x$ . - $x=|y-3|$

For the given function, find $\frac{f(x+h)-f(x)}{h}$ . - $x^{2}+2$