Question 1

Use the graph to answer the question.
-Find the domain and range of the rational function graphed below.

Accepted Answer

A)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty ) ;$ Range: $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty ) ;$ Range: $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , \infty )$

Question 2

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = x ^ { 3 } - ( 4 + 2 i ) x ^ { 2 } + ( - 5 + 8 i ) x + 10 i ; k = 2 i$$

Accepted Answer

A)  $f ( x ) = ( x - i ) ( x + 1 ) ( x - 10 )$ 
B)  $f ( x ) = ( x + 2 i ) ( x - 1 ) ( x - 5 )$ 
C)  $f ( x ) = ( x - 2 i ) ( x + 1 ) ( x - 5 )$ 
D)  $f ( x ) = ( x - 2 i ) ( x - 1 ) ( x + 5 )$ 
A)  $f ( x ) = ( x - i ) ( x + 1 ) ( x - 10 )$ 
B)  $f ( x ) = ( x + 2 i ) ( x - 1 ) ( x - 5 )$ 
C)  $f ( x ) = ( x - 2 i ) ( x + 1 ) ( x - 5 )$ 
D)  $f ( x ) = ( x - 2 i ) ( x - 1 ) ( x + 5 )$

Question 3

Solve the problem.
-John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 12 x + 44$, with $P$ being profits and $x$ the number of hotdogs sold. What is the most he can earn?

Accepted Answer

A)  $\$ 80$ 
B)  $\$ 36$ 
C)  $\$ 104$ 
D)  $\$ 68$ 
A)  $\$ 80$ 
B)  $\$ 36$ 
C)  $\$ 104$ 
D)  $\$ 68$

Question 4

Solve the problem.
-The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 69,000 mi has $\frac { 1 } { 16 }$ in. of tread left. How much tread will be left on a tire that has traveled 46,000 mi?

Accepted Answer

A)  $1,104,000 \mathrm { in }$. 
B)  $\frac { 32 } { 3 } \mathrm { in }$. 
C)  $\frac { 3 } { 32 } \mathrm { in }$. 
D)  $\frac { 1 } { 1104000 }$ in. 
A)  $1,104,000 \mathrm { in }$. 
B)  $\frac { 32 } { 3 } \mathrm { in }$. 
C)  $\frac { 3 } { 32 } \mathrm { in }$. 
D)  $\frac { 1 } { 1104000 }$ in.

Question 5

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } - 18 x + 87$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $[ 6 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 9 , \infty )$ 
C)  Domain: $[ 6 , \infty )$; Range: $( - \infty , 9 ]$ 
D)  Domain: $[ 6 , \infty )$; Range: $( - \infty , 0 ]$ 
A)  Domain: $( - \infty , \infty )$; Range: $[ 6 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 9 , \infty )$ 
C)  Domain: $[ 6 , \infty )$; Range: $( - \infty , 9 ]$ 
D)  Domain: $[ 6 , \infty )$; Range: $( - \infty , 0 ]$

Question 6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$\frac { 1 } { 2 } ; f ( x ) = 2 x ^ { 4 } - 21 x ^ { 3 } + 3 x + 1$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 7

Answer the question
-If y varies inversely as the square of x, and x is tripled, how is y changed?

Accepted Answer

A)  y is nine times as large as before 
B)  y is one-third as large as before 
C)  y is three times as large as before 
D)  y is one-ninth as large as before 
A)  y is nine times as large as before 
B)  y is one-third as large as before 
C)  y is three times as large as before 
D)  y is one-ninth as large as before

Question 8

Answer the question
-What type of variation is suggested by the graph?

Accepted Answer

A)  $y$ varies inversely as $x$ 
B)  $y$ varies directly as the square of $x$ 
C)  $y$ varies inversely as the square of $x$ 
D)  $y$ varies directly as $x$ 
A)  $y$ varies inversely as $x$ 
B)  $y$ varies directly as the square of $x$ 
C)  $y$ varies inversely as the square of $x$ 
D)  $y$ varies directly as $x$

Question 9

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = - \frac { 1 } { ( x - 2 ) ^ { 2 } }$$

Accepted Answer

A)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 1 )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 0 )$ 
D)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , 0 )$ 
A)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 1 )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 0 )$ 
D)  Domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$; Range: $( - \infty , 0 )$

Question 10

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

Accepted Answer

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

Question 11

Solve.
-A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years.

Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$ 
B)  $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$ 
C)  $f ( x ) = 0.94 x + 7.08$ 
D)  $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$ 
A)  $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$ 
B)  $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$ 
C)  $f ( x ) = 0.94 x + 7.08$ 
D)  $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$

Question 12

Solve the problem.
-A piece of rectangular sheet metal is 4 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of $x$ will the area of the cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary, round to 2 decimal places.

Accepted Answer

A)  8 in. 
B)  $16 \mathrm { in }$. 
C)  1 in. 
D)  2 in. 
A)  8 in. 
B)  $16 \mathrm { in }$. 
C)  1 in. 
D)  2 in.

Question 13

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

Accepted Answer

A)  $f ( 1.7 ) = 0.3421$ and $f ( 1.8 ) = - 0.6624$ 
B)  $\mathrm { f } ( 1.7 ) = 0.3421$ and $\mathrm { f } ( 1.8 ) = 0.6624$ 
C)  $f ( 1.7 ) = - 0.3421$ and $f ( 1.8 ) = - 0.6624$ 
D)  $f ( 1.7 ) = 0.6579$ and $f ( 1.8 ) = - 0.6624$ 
A)  $f ( 1.7 ) = 0.3421$ and $f ( 1.8 ) = - 0.6624$ 
B)  $\mathrm { f } ( 1.7 ) = 0.3421$ and $\mathrm { f } ( 1.8 ) = 0.6624$ 
C)  $f ( 1.7 ) = - 0.3421$ and $f ( 1.8 ) = - 0.6624$ 
D)  $f ( 1.7 ) = 0.6579$ and $f ( 1.8 ) = - 0.6624$

Question 14

Solve the problem.
-If an object is thrown upward with an initial velocity of $16 \mathrm { ft } / \mathrm { sec }$, its height after $\mathrm { t }$ sec is given by $s ( t ) = 16 t - 16 t ^ { 2 }$. Find the maximum height attained by the object. (The object will attain maximum height exactly at the halfway point in terms of the time $t$, where $t = 0$ is at the beginning of the object's flight, and the final time is when the object hits the ground.)

Accepted Answer

A)  $16 \mathrm { ft }$ 
B)  $4 \mathrm { ft }$ 
C)  $- 12 \mathrm { ft }$ 
D)  $0 \mathrm { ft }$ 
A)  $16 \mathrm { ft }$ 
B)  $4 \mathrm { ft }$ 
C)  $- 12 \mathrm { ft }$ 
D)  $0 \mathrm { ft }$

Question 15

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - x ^ { 3 } + 15 x ^ { 2 } + x - 10$ 
B)  $P ( x ) = - x ^ { 5 } - 5 x ^ { 3 } - 6 x ^ { 2 } + 10 x$ 
C)  $P ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 6 x ^ { 2 } + x + 10$ 
D)  $P ( x ) = x ^ { 5 } + 3 x ^ { 4 } - 5 x ^ { 3 } - 15 x ^ { 2 } + x + 10$ 
A)  $P ( x ) = - x ^ { 3 } + 15 x ^ { 2 } + x - 10$ 
B)  $P ( x ) = - x ^ { 5 } - 5 x ^ { 3 } - 6 x ^ { 2 } + 10 x$ 
C)  $P ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 6 x ^ { 2 } + x + 10$ 
D)  $P ( x ) = x ^ { 5 } + 3 x ^ { 4 } - 5 x ^ { 3 } - 15 x ^ { 2 } + x + 10$

Question 16

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 3 x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4$$

Accepted Answer

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

Question 17

Solve the problem. Round your answer to two decimal places.
-The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 72 seconds are required to make a 3-by-4 enlargement, find the time required
For a 6-by-7 enlargement.

Accepted Answer

A)  336 sec 
B)  210 sec 
C)  294 sec 
D)  252 sec 
A)  336 sec 
B)  210 sec 
C)  294 sec 
D)  252 sec

Question 18

Graph the function.
-$f(x)=-\frac{1}{x+4}$

Accepted Answer

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

Question 19

Solve the problem.
-The following polynomial approximates the rabbit population in a particular area. $R ( x ) = - 0.121 x ^ { 5 } + 3.133 x ^ { 4 } + 4500$, where $x$ is the number of years from year 0 . Use a graphing calculator to describe the rabbit population from the years 0 to 25 .

Accepted Answer

A)  The population remains stable. 
B)  The population decreases. 
C)  The population increases. 
A)  The population remains stable. 
B)  The population decreases. 
C)  The population increases.

Question 20

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=x(x-1)(x+2)^{3}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Use the graph to answer the question. -Find the domain and range of the rational function graphed below.

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - ( 4 + 2 i ) x ^ { 2 } + ( - 5 + 8 i ) x + 10 i ; k = 2 i$

Solve the problem. -John owns a hotdog stand. His profit is represented by the equation $P ( x ) = - x ^ { 2 } + 12 x + 44$ , with $P$ being profits and $x$ the number of hotdogs sold. What is the most he can earn?

Solve the problem. -The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled 69,000 mi has $\frac { 1 } { 16 }$ in. of tread left. How much tread will be left on a tire that has traveled 46,000 mi?

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } - 18 x + 87$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $\frac { 1 } { 2 } ; f ( x ) = 2 x ^ { 4 } - 21 x ^ { 3 } + 3 x + 1$

Answer the question -If y varies inversely as the square of x, and x is tripled, how is y changed?

Answer the question -What type of variation is suggested by the graph?

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 2 ) ^ { 2 } }$

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

Solve. -A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = x ^ { 4 } - 9 x ^ { 2 } + 18 ; 1.7$ and $1.8$

Find the equation that the given graph represents. -

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 6 } - x ^ { 5 } + 7 x ^ { 2 } - 4$

Solve the problem. Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 72 seconds are required to make a 3-by-4 enlargement, find the time required For a 6-by-7 enlargement.

Graph the function. - $f(x)=-\frac{1}{x+4}$ $Graph the function. - f(x)=-\frac{1}{x+4}$

Solve the problem. -The following polynomial approximates the rabbit population in a particular area. $R ( x ) = - 0.121 x ^ { 5 } + 3.133 x ^ { 4 } + 4500$ , where $x$ is the number of years from year 0 . Use a graphing calculator to describe the rabbit population from the years 0 to 25 .

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x(x-1)(x+2)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x-1)(x+2)^{3}$

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

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Exam 3: Polynomial and Rational Functions