Question 1

Graph.
-$f(x)=-\frac{4}{7}(x+4)^{2}+2$

Accepted Answer

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

Question 2

Write the word or phrase that best completes each statement or answers the question
-The average waiting time in a line before getting served is given by
$$W=\frac{S(S-A)}{A}$$
where $\mathrm{A}$ is the average rate that people arrive at the line and $\mathrm{S}$ is the average service time. At a certain bank, the average service time is 4 minutes. By sketching a graph of the equation on the interval $(0,4]$, answer the following questions. What happens to $W$ when A is close to zero? Why does this make sense? What feature of your graph gives this information?

Accepted Answer

Answers will vary. Possible answer: As A

Question 3

Solve the problem.
-Suppose that the speed (in $m / s e c)$ of a particle moving on the $x$-axis at time $t$ seconds ( $t \geq 0$ ) is given by:
$$V(t)=t^{3}-8 t^{2}+15 t+10$$
Find V(4).

Accepted Answer

A)  $6 \mathrm{~m} / \mathrm{sec}$ 
B)  $11 \mathrm{~m} / \mathrm{sec}$ 
C)  $21 \mathrm{~m} / \mathrm{sec}$ 
D)  $16 \mathrm{~m} / \mathrm{sec}$ 
A)  $6 \mathrm{~m} / \mathrm{sec}$ 
B)  $11 \mathrm{~m} / \mathrm{sec}$ 
C)  $21 \mathrm{~m} / \mathrm{sec}$ 
D)  $16 \mathrm{~m} / \mathrm{sec}$

Question 4

Solve the problem.
-A charter flight charges a fare of $\$ 400$ per person plus $\$ 3$ per person for each unsold seat on the plane. If the plane holds 213 passengers and if $x$ represents the number of unsold seats, find an expression for the total revenue received for the flight. (Hint: multiply the number of seats sold, 213 - $x$, by the price per ticket).

Accepted Answer

A)  $R(x)=x(213-x)$ 
B)  $R(x)=(213-x)(400+3)$ 
C)  $R(x)=(213-x)(400+3 x)$ 
D)  $R(x)=x(400+3 x)$ 
A)  $R(x)=x(213-x)$ 
B)  $R(x)=(213-x)(400+3)$ 
C)  $R(x)=(213-x)(400+3 x)$ 
D)  $R(x)=x(400+3 x)$

Question 5

Graph the function.
-$f(x)=[-x+3]$

Accepted Answer

A)    
B)    
A)    
B)

Question 6

Determine whether the following rule defines $y$ as a function of $x$.
-$y=\sqrt{6 x-3}$

Accepted Answer

A) True 
 B)False

Question 7

Solve the problem.
-Suppose that the speed (in $\mathrm{m} / \mathrm{sec}$ ) of a particle moving on the $x$-axis at time $t$ seconds ( $t \geq 0$ ) is given by:
$$V(t)=t^{3}-8 t^{2}+15 t+10$$
By sketching a graph of $C(t)$, estimate during what time period the speed of the particle is less than $10 \mathrm{~m} / \mathrm{sec}$.

Accepted Answer

A)  Between about $t=4$ and $t=5$ seconds 
B)  Between about $t=2$ and $t=4$ seconds 
C)  Between about $t=4$ and $t=6$ seconds 
D)  Between about $t=3$ and $t=5$ seconds 
A)  Between about $t=4$ and $t=5$ seconds 
B)  Between about $t=2$ and $t=4$ seconds 
C)  Between about $t=4$ and $t=6$ seconds 
D)  Between about $t=3$ and $t=5$ seconds

Question 8

Write a cost function for the problem. Assume that the relationship is linear.
-A cab company charges a base rate of $\$ 1.50$ plus 15 cents per minute. Let $C(x)$ be the cost in dollars of using the cab for $x$ minutes.

Accepted Answer

A)  $C(x)=1.50 x+0.15$ 
B)  $C(x)=0.15 x+1.50$ 
C)  $C(x)=1.50 x-0.15$ 
D)  $C(x)=0.15 x-1.50$ 
A)  $C(x)=1.50 x+0.15$ 
B)  $C(x)=0.15 x+1.50$ 
C)  $C(x)=1.50 x-0.15$ 
D)  $C(x)=0.15 x-1.50$

Question 9

Solve the problem.
-In deciding whether or not to set up a new manufacturing plant, analysts for a popcorn company have decided that a linear function is a reasonable estimation for the total $\operatorname{cost} \mathrm{C}(\mathrm{x})$ in dollars to produce $x$ bags of microwave popcorn. They estimate the cost to produce 10,000 bags as $\$ 5250$ and the cost to produce 15,000 bags as $\$ 7530$. Find the marginal cost of the bags of microwave popcorn to be produced in this plant.

Accepted Answer

A)  $\$ 45.6$ 
B)  $\$ 4.56$ 
C)  $\$ 2280$ 
D)  $\$ 0.456$ 
A)  $\$ 45.6$ 
B)  $\$ 4.56$ 
C)  $\$ 2280$ 
D)  $\$ 0.456$

Question 10

Graph the polynomial function.
-$f(x)=-x^{4}+x^{2}$

Accepted Answer

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

Question 11

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 $f(x)=\sqrt{x^{2}+4 x-2}$ at 2.1, 2.5, 2.9, 3.3, 3.7, 4.1.

Accepted Answer

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

Question 12

Graph the polynomial function.
-$f(x)=x^{3}-4$

Accepted Answer

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

Question 13

State whether the parabola opens upward or downward.
-$f(x)=-9(x-2)^{2}-2$

Accepted Answer

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

Question 14

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.
-$f(x)=x^{3}-4 x^{2}-x+4$

Accepted Answer

Answers wi

Question 15

Solve the problem.
-Suppose that the population of a certain city during a certain time period can be approximated by:
$$P(x)=-0.1 x^{5}+3.7 x^{4}+4000$$
Where $x$ is time in years since 1960 . Find $P(3)$.

Accepted Answer

A)  8775 
B)  3375 
C)  4275 
D)  7075 
A)  8775 
B)  3375 
C)  4275 
D)  7075

Question 16

Solve the problem.
-Midtown Delivery Service delivers packages which cost $\$ 1.30$ per package to deliver. The fixed cost to run the delivery truck is $\$ 70$ per day. If the company charges $\$ 8.30$ per package, how many packages must be delivered daily to reach the break-even point?

Accepted Answer

A)  53 packages 
B)  6 packages 
C)  7 packages 
D)  10 packages 
A)  53 packages 
B)  6 packages 
C)  7 packages 
D)  10 packages

Question 17

Write the word or phrase that best completes each statement or answers the question
-A company has fixed costs of $\$ 2300$ and a marginal cost of $\$ 3.76$ per unit. Find the average cost function (i.e. the average cost per unit to produce $x$ units). What is the horizontal asymptote of the graph of the average cost function? What information is provided by the horizontal asymptote?

Accepted Answer

@#LAT-DLM&
The horizontal asymptote is @#LAT-DLM&.

Question 18

Solve the problem.
-Suppose the price $p$ of bolts is related to the quantity $q$ that is demanded by:
$$p=550-5 q^{2}$$
Where $\mathrm{q}$ is measured in hundreds of bolts. Find the price when the number of bolts demanded is 700 .

Accepted Answer

A)  $\$ 325$ 
B)  $\$ 315$ 
C)  $\$ 320$ 
D)  $\$ 305$ 
A)  $\$ 325$ 
B)  $\$ 315$ 
C)  $\$ 320$ 
D)  $\$ 305$

Question 19

Give the equation of the vertical asymptote(s) of the rational function.
-$g(x)=\frac{x-9}{x^{2}+2 x}$

Accepted Answer

A)  $x=9$ 
B)  $x=0, x=-2$ 
C)  $x=2$ 
D)  $x=-2$ 
A)  $x=9$ 
B)  $x=0, x=-2$ 
C)  $x=2$ 
D)  $x=-2$

Question 20

Solve the problem.
-A cereal factory has weekly fixed costs of $\$ 22,000$. It costs $\$ 1.26$ to produce each box of cereal. A box of cereal sells for $\$ 3.87$. Find the rule of the revenue function $r(x)$ that gives the total weekly revenue from selling $x$ boxes of cereal.

Accepted Answer

A)  $c(x)=22,000+2.61 x$ 
B)  $c(x)=3.87 x$ 
C)  $c(x)=2.61 x$ 
D)  $c(x)=22,000+3.87 x$ 
A)  $c(x)=22,000+2.61 x$ 
B)  $c(x)=3.87 x$ 
C)  $c(x)=2.61 x$ 
D)  $c(x)=22,000+3.87 x$

Graph. - $f(x)=-\frac{4}{7}(x+4)^{2}+2$ $Graph. - f(x)=-\frac{4}{7}(x+4)^{2}+2$

Solve the problem. -Suppose that the speed (in $m / s e c)$ of a particle moving on the $x$ -axis at time $t$ seconds ( $t \geq 0$ ) is given by: $V(t)=t^{3}-8 t^{2}+15 t+10$ Find V(4).

Graph the function. - $f(x)=[-x+3]$

Determine whether the following rule defines $y$ as a function of $x$ . - $y=\sqrt{6 x-3}$

Write a cost function for the problem. Assume that the relationship is linear. -A cab company charges a base rate of $\$ 1.50$ plus 15 cents per minute. Let $C(x)$ be the cost in dollars of using the cab for $x$ minutes.

Graph the polynomial function. - $f(x)=-x^{4}+x^{2}$ $Graph the polynomial function. - f(x)=-x^{4}+x^{2}$

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 $f(x)=\sqrt{x^{2}+4 x-2}$ at 2.1, 2.5, 2.9, 3.3, 3.7, 4.1.

Graph the polynomial function. - $f(x)=x^{3}-4$ $Graph the polynomial function. - f(x)=x^{3}-4$

State whether the parabola opens upward or downward. - $f(x)=-9(x-2)^{2}-2$

Solve the problem. -Suppose that the population of a certain city during a certain time period can be approximated by: $P(x)=-0.1 x^{5}+3.7 x^{4}+4000$ Where $x$ is time in years since 1960 . Find $P(3)$ .

Solve the problem. -Midtown Delivery Service delivers packages which cost $\$ 1.30$ per package to deliver. The fixed cost to run the delivery truck is $\$ 70$ per day. If the company charges $\$ 8.30$ per package, how many packages must be delivered daily to reach the break-even point?

Solve the problem. -Suppose the price $p$ of bolts is related to the quantity $q$ that is demanded by: $p=550-5 q^{2}$ Where $\mathrm{q}$ is measured in hundreds of bolts. Find the price when the number of bolts demanded is 700 .

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x-9}{x^{2}+2 x}$

Solve the problem. -A cereal factory has weekly fixed costs of $\$ 22,000$ . It costs $\$ 1.26$ to produce each box of cereal. A box of cereal sells for $\$ 3.87$ . Find the rule of the revenue function $r(x)$ that gives the total weekly revenue from selling $x$ boxes of cereal.

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

Graph. - f(x)=−47(x+4)2+2f(x)=-\frac{4}{7}(x+4)^{2}+2f(x)=−74​(x+4)2+2

Solve the problem. -Suppose that the speed (in m/sec)m / s e c)m/sec) of a particle moving on the xxx -axis at time ttt seconds ( t≥0t \geq 0t≥0 ) is given by: V(t)=t3−8t2+15t+10V(t)=t^{3}-8 t^{2}+15 t+10V(t)=t3−8t2+15t+10 Find V(4).

Graph the function. - f(x)=[−x+3]f(x)=[-x+3]f(x)=[−x+3]

Determine whether the following rule defines yyy as a function of xxx . - y=6x−3y=\sqrt{6 x-3}y=6x−3​

Write a cost function for the problem. Assume that the relationship is linear. -A cab company charges a base rate of $1.50\$ 1.50$1.50 plus 15 cents per minute. Let C(x)C(x)C(x) be the cost in dollars of using the cab for xxx minutes.

Graph the polynomial function. - f(x)=−x4+x2f(x)=-x^{4}+x^{2}f(x)=−x4+x2

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)=x2+4x−2f(x)=\sqrt{x^{2}+4 x-2}f(x)=x2+4x−2​ at 2.1, 2.5, 2.9, 3.3, 3.7, 4.1.

Graph the polynomial function. - f(x)=x3−4f(x)=x^{3}-4f(x)=x3−4

State whether the parabola opens upward or downward. - f(x)=−9(x−2)2−2f(x)=-9(x-2)^{2}-2f(x)=−9(x−2)2−2

Solve the problem. -Suppose that the population of a certain city during a certain time period can be approximated by: P(x)=−0.1x5+3.7x4+4000P(x)=-0.1 x^{5}+3.7 x^{4}+4000P(x)=−0.1x5+3.7x4+4000 Where xxx is time in years since 1960 . Find P(3)P(3)P(3) .

Solve the problem. -Suppose the price ppp of bolts is related to the quantity qqq that is demanded by: p=550−5q2p=550-5 q^{2}p=550−5q2 Where q\mathrm{q}q is measured in hundreds of bolts. Find the price when the number of bolts demanded is 700 .

Give the equation of the vertical asymptote(s) of the rational function. - g(x)=x−9x2+2xg(x)=\frac{x-9}{x^{2}+2 x}g(x)=x2+2xx−9​

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

Graph. - $f(x)=-\frac{4}{7}(x+4)^{2}+2$ $Graph. - f(x)=-\frac{4}{7}(x+4)^{2}+2$

Solve the problem. -Suppose that the speed (in $m / s e c)$ of a particle moving on the $x$ -axis at time $t$ seconds ( $t \geq 0$ ) is given by: $V(t)=t^{3}-8 t^{2}+15 t+10$ Find V(4).

Graph the function. - $f(x)=[-x+3]$

Determine whether the following rule defines $y$ as a function of $x$ . - $y=\sqrt{6 x-3}$

Write a cost function for the problem. Assume that the relationship is linear. -A cab company charges a base rate of $\$ 1.50$ plus 15 cents per minute. Let $C(x)$ be the cost in dollars of using the cab for $x$ minutes.

Graph the polynomial function. - $f(x)=-x^{4}+x^{2}$ $Graph the polynomial function. - f(x)=-x^{4}+x^{2}$

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 $f(x)=\sqrt{x^{2}+4 x-2}$ at 2.1, 2.5, 2.9, 3.3, 3.7, 4.1.

Graph the polynomial function. - $f(x)=x^{3}-4$ $Graph the polynomial function. - f(x)=x^{3}-4$

State whether the parabola opens upward or downward. - $f(x)=-9(x-2)^{2}-2$

Solve the problem. -Suppose that the population of a certain city during a certain time period can be approximated by: $P(x)=-0.1 x^{5}+3.7 x^{4}+4000$ Where $x$ is time in years since 1960 . Find $P(3)$ .

Solve the problem. -Suppose the price $p$ of bolts is related to the quantity $q$ that is demanded by: $p=550-5 q^{2}$ Where $\mathrm{q}$ is measured in hundreds of bolts. Find the price when the number of bolts demanded is 700 .

Give the equation of the vertical asymptote(s) of the rational function. - $g(x)=\frac{x-9}{x^{2}+2 x}$