Question 1

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 4 x - 7 } { x - 9 }$$

Accepted Answer

A)  $y = x + 13$ 
B)  $x = y + 13$ 
C)  none 
D)  $y = x - 5$ 
A)  $y = x + 13$ 
B)  $x = y + 13$ 
C)  none 
D)  $y = x - 5$

Question 2

Answer the question
-Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?

Accepted Answer

A)  z is multiplied by $$\frac { 3 } { 2 }$$ 
B)  z is six times as large as before 
C)  z is one-twelfth as large as before 
D)  z is one-sixth as large as before 
A)  z is multiplied by $$\frac { 3 } { 2 }$$ 
B)  z is six times as large as before 
C)  z is one-twelfth as large as before 
D)  z is one-sixth as large as before

Question 3

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 6 , i , - i$ and $P ( - 3 ) = 60$

Accepted Answer

A)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } - 2 x - 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } - 2 x - 12$ 
C)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } + 2 x + 12$ 
D)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } + 2 x + 12$ 
A)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } - 2 x - 12$ 
B)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } - 2 x - 12$ 
C)  $P ( x ) = - 2 x ^ { 3 } - 12 x ^ { 2 } + 2 x + 12$ 
D)  $P ( x ) = 2 x ^ { 3 } + 12 x ^ { 2 } + 2 x + 12$

Question 4

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-1)^{2}+3$

Find the domain and range.

Accepted Answer

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

Question 5

Factor f(x) into linear factors given that k is a zero of f(x).
-$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 6 ; k = 1$$

Accepted Answer

A)  $( x + 1 ) ( x + 2 ) ( 2 x - 3 )$ 
B)  $( x - 1 ) ( x + 1 ) ( 2 x - 6 )$ 
C)  $( x - 1 ) ( x + 2 ) ( 2 x - 3 )$ 
D)  $( x - 1 ) ( x - 2 ) ( 2 x + 3 )$ 
A)  $( x + 1 ) ( x + 2 ) ( 2 x - 3 )$ 
B)  $( x - 1 ) ( x + 1 ) ( 2 x - 6 )$ 
C)  $( x - 1 ) ( x + 2 ) ( 2 x - 3 )$ 
D)  $( x - 1 ) ( x - 2 ) ( 2 x + 3 )$

Question 6

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the
indicated domain interval. Give answers to the nearest hundredth.
-$$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 26 x - 72 ; [ 1,2 ]$$

Accepted Answer

A)  $( - 6.09,120.09 )$ 
B)  $( 3.00 , - 60.00 )$ 
C)  $( 0,8 )$ 
D)  $( 1.42 , - 91.94 )$ 
A)  $( - 6.09,120.09 )$ 
B)  $( 3.00 , - 60.00 )$ 
C)  $( 0,8 )$ 
D)  $( 1.42 , - 91.94 )$

Question 7

Provide an appropriate response.
-Explain the behavior of the graph of $\mathrm { f } ( \mathrm { x } )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { x - 9 }$

Accepted Answer

A)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
B)  Approaches $\infty$ from the left and the right 
C)  Approaches $- \infty$ from the left and the right 
D)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
A)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
B)  Approaches $\infty$ from the left and the right 
C)  Approaches $- \infty$ from the left and the right 
D)  Approaches $\infty$ from the left, approaches $- \infty$ from the right

Question 8

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = - x ^ { 5 } - 6 x ^ { 3 } - 8 x + 4$$

Accepted Answer

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

Question 9

Determine whether the statement is true or false.
-$$\text { If } \mathrm { c } \text { and } \mathrm { d } \text { are complex numbers, then } \overline { \mathrm { c } - \mathrm { d } } = \overline { \mathrm { c } } - \overline { \mathrm { d } }$$

Accepted Answer

A) True 
 B)False

Question 10

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$I = P R T$, where $I$ is the simple interest on a principal of $P$ dollars invested for $T$ years at an interest rate of $R$ per year

Accepted Answer

Simple interest vari

Question 11

Sketch the graph of the rational function.
-$f(x)=\frac{x-2}{x+3}$

Accepted Answer

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

Question 12

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = \pm 3$; horizontal: $y = - 4 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  Vertical: $x = - 4$; horizontal: $y = \pm 3 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
C)  Vertical: $x = \pm 3$; horizontal: $y = - 4 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = - 4$; horizontal: $y = \pm 3 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
A)  Vertical: $x = \pm 3$; horizontal: $y = - 4 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  Vertical: $x = - 4$; horizontal: $y = \pm 3 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
C)  Vertical: $x = \pm 3$; horizontal: $y = - 4 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = - 4$; horizontal: $y = \pm 3 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$

Question 13

Solve the problem. Round your answer to two decimal places.
-The distance to the horizon varies directly as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 25 feet, how far can a person see from a
Height of 49 feet?

Accepted Answer

A)  8.4 mi 
B)  7.7 mi 
C)  9.6 mi 
D)  8.7 mi 
A)  8.4 mi 
B)  7.7 mi 
C)  9.6 mi 
D)  8.7 mi

Question 14

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
-$$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 6$$

Accepted Answer

A)  $3 , - 3,2 , - 2$ 
B)  $1.7 , - 1.7,1.4 , - 1.4$ 
C)  $1.7,1.4$ 
D)  $- 1,1.8,1.8 , - 1.8$ 
A)  $3 , - 3,2 , - 2$ 
B)  $1.7 , - 1.7,1.4 , - 1.4$ 
C)  $1.7,1.4$ 
D)  $- 1,1.8,1.8 , - 1.8$

Question 15

Use synthetic division to perform the division.
-$$\frac { 3 x ^ { 3 } - 13 x ^ { 2 } - 35 x + 30 } { x - 6 }$$

Accepted Answer

A)  $3 x ^ { 2 } + 5 x - 5$ 
B)  $3 x + 5$ 
C)  $\frac { 1 } { 2 } x ^ { 2 } + - \frac { 13 } { 6 } x + - \frac { 35 } { 6 }$ 
D)  $- 3 x ^ { 2 } + 6 x - 5$ 
A)  $3 x ^ { 2 } + 5 x - 5$ 
B)  $3 x + 5$ 
C)  $\frac { 1 } { 2 } x ^ { 2 } + - \frac { 13 } { 6 } x + - \frac { 35 } { 6 }$ 
D)  $- 3 x ^ { 2 } + 6 x - 5$

Question 16

Sketch the graph of the parabola.
-$y=-2 x^{2}+2 x+2$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { x + 8 }$$

Accepted Answer

A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty ) ;$ Range: $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty ) ;$ Range: $( - \infty , - 8 ) \cup ( - 8 , \infty )$

Question 19

Solve the problem.
-A coin is tossed upward from a balcony 242 feet high with an initial velocity of 16 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 16 t + 242$. During what interval of time will the coin be at a height of at least $50 \mathrm { ft }$ ?

Accepted Answer

A)  $4 \leq t \leq 8$ 
B)  $3 \leq t \leq 4$ 
C)  $0 \leq t \leq 1$ 
D)  $0 \leq t \leq 4$ 
A)  $4 \leq t \leq 8$ 
B)  $3 \leq t \leq 4$ 
C)  $0 \leq t \leq 1$ 
D)  $0 \leq t \leq 4$

Question 20

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$\mathrm { P } = \mathrm { nb } \text {, where } \mathrm { P } \text { is the perimeter of a regular polygon with } \mathrm { n } \text { sides each of length }$$

Accepted Answer

The perimeter of a regular pol

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 4 x - 7 } { x - 9 }$

Answer the question -Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 6 , i , - i$ and $P ( - 3 ) = 60$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-1)^{2}+3$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-1)^{2}+3 Find the domain and range.$ Find the domain and range.

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 6 ; k = 1$

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 26 x - 72 ; [ 1,2 ]$

Provide an appropriate response. -Explain the behavior of the graph of $\mathrm { f } ( \mathrm { x } )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 1 } { x - 9 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 6 x ^ { 3 } - 8 x + 4$

Determine whether the statement is true or false. - $\text { If } \mathrm { c } \text { and } \mathrm { d } \text { are complex numbers, then } \overline { \mathrm { c } - \mathrm { d } } = \overline { \mathrm { c } } - \overline { \mathrm { d } }$

Translate the given formula to an English phrase using the word ʺvariesʺ. - $I = P R T$ , where $I$ is the simple interest on a principal of $P$ dollars invested for $T$ years at an interest rate of $R$ per year

Sketch the graph of the rational function. - $f(x)=\frac{x-2}{x+3}$ $Sketch the graph of the rational function. - f(x)=\frac{x-2}{x+3}$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Solve the problem. Round your answer to two decimal places. -The distance to the horizon varies directly as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 25 feet, how far can a person see from a Height of 49 feet?

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 6$

Use synthetic division to perform the division. - $\frac { 3 x ^ { 3 } - 13 x ^ { 2 } - 35 x + 30 } { x - 6 }$

Sketch the graph of the parabola. - $y=-2 x^{2}+2 x+2$ $Sketch the graph of the parabola. - y=-2 x^{2}+2 x+2$

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

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { x + 8 }$

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { P } = \mathrm { nb } \text {, where } \mathrm { P } \text { is the perimeter of a regular polygon with } \mathrm { n } \text { sides each of length }$

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

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Give the equation of any oblique asymptotes. - f(x)=x2+4x−7x−9f ( x ) = \frac { x ^ { 2 } + 4 x - 7 } { x - 9 }f(x)=x−9x2+4x−7​