Question 1

Use the Remainder Theorem to find   for   and   .

Accepted Answer

A) -2 
B) 0 
C) 10 
D) -10 
E) -12 
A) -2 
B) 0 
C) 10 
D) -10 
E) -12

Question 2

Use translation and/or reflection concepts to explain how the graph of P can be used to produce the graph of Q .

Accepted Answer

A) Shift the graph of P     unit to the left. 
B) Shift the graph of P     unit . 
C) Shift the graph of P     unit . 
D) Shift the graph of P horizontally   unit to the right. 
A) Shift the graph of P     unit to the left. 
B) Shift the graph of P     unit . 
C) Shift the graph of P     unit . 
D) Shift the graph of P horizontally   unit to the right.

Question 3

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by   where t is the number of months after the CD is released. Use S to predict the month in which sales are expected to reach a maximum.

Accepted Answer

A) Sales will reach a maximum in the fifth month. 
B) Sales will reach a maximum in the tenth month. 
C) Sales will reach a maximum in the third month. 
D) Sales will reach a maximum in the eleventh month. 
E) Sales will reach a maximum in the sixth month. 
A) Sales will reach a maximum in the fifth month. 
B) Sales will reach a maximum in the tenth month. 
C) Sales will reach a maximum in the third month. 
D) Sales will reach a maximum in the eleventh month. 
E) Sales will reach a maximum in the sixth month.

Question 4

Write   as the product of   and its reduced polynomial.

Accepted Answer

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

Question 5

Find the real zeros of the polynomial function   by factoring.

Accepted Answer

A) 1, -2, -24 
B) 1, -6, 4 
C) 0, -12, -2 
D) 0, 6, -4 
E) 0, 12, 2 
A) 1, -2, -24 
B) 1, -6, 4 
C) 0, -12, -2 
D) 0, 6, -4 
E) 0, 12, 2

Question 6

Use synthetic division to determine which of the following values of c is a zero of   . 7, 7, 4, 3, 6

Accepted Answer

A) -3 
B) -6 
C) 7 
D) 4 
E) -7 
A) -3 
B) -6 
C) 7 
D) 4 
E) -7

Question 7

Find a polynomial function of lowest degree with integer coefficients that has the zeros 8, -1, -2.

Accepted Answer

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

Question 8

A cylindrical soft drink can is to be made so that it will have a volume of 203 milliliters. If r is the radius of the can in centimeters, then the total surface area A of the can is given by the rational function   . Does the graph of A have a slant asymptote?

Accepted Answer

A) True 
 B)False

Question 9

Determine the vertical and slant asymptotes of the rational function below.

Accepted Answer

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

Question 10

Find all the zeros of the polynomial function   and write the polynomial as a product of its linear factors.

Accepted Answer

A) 5, 2 + 2 i, 2 + 2 i;   
B) 5,   ,   ;   
C) 5, 2 2 i, 2 + 2 i ;   
D) 5, 2 2 i, 2 2 i ;   
E) 5, 2 2 i, 2 + 2 i ;   
A) 5, 2 + 2 i, 2 + 2 i;   
B) 5,   ,   ;   
C) 5, 2 2 i, 2 + 2 i ;   
D) 5, 2 2 i, 2 2 i ;   
E) 5, 2 2 i, 2 + 2 i ;

Question 11

A company constructs boxes from rectangular pieces of cardboard that measure 14 inches by 10 inches. An open box is formed by cutting squares that measure x inches by x inches from each corner of the cardboard and folding up the sides. Determine (to the nearest tenth of an inch)the x value that maximizes the volume of the box.

Accepted Answer

A)    inches 
B) 2.2 inches 
C) 2.7 inches 
D) 3.8 inches 
E) 1.9 inches 
A)    inches 
B) 2.2 inches 
C) 2.7 inches 
D) 3.8 inches 
E) 1.9 inches

Question 12

Find the zeros of the polynomial function   . If a zero is a multiple zero, state its multiplicity.

Accepted Answer

A) -1, -12, 2 
B) 0, -6, 4 
C) -3, 2, 4 
D) 3, -2, -4 
E) 1, -6, -4 
A) -1, -12, 2 
B) 0, -6, 4 
C) -3, 2, 4 
D) 3, -2, -4 
E) 1, -6, -4

Question 13

Use the Rational Zero Theorem to list all possible rational zeros of the polynomial function   .

Accepted Answer

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

Question 14

Find a polynomial function P of degree 3 with integer coefficients that has zeros   and   .

Accepted Answer

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

Question 15

Find a polynomial function of degree 4 with integer coefficients, whose leading coefficient is equal to one, and that has the zeros   and   .

Accepted Answer

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

Question 16

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and the volume of the tank is   cubic feet. Find, to the nearest thousandth of a foot, the length of the radius x.

Accepted Answer

A)    ft 
B)    ft 
C)    ft 
D) 1.041 ft 
E)    ft 
A)    ft 
B)    ft 
C)    ft 
D) 1.041 ft 
E)    ft

Question 17

A cube measures n inches on each edge. If a slice 5 inches thick is cut from one face of the cube, the resulting solid has a volume of 2250 cubic inches. Find n .

Accepted Answer

A) 16 inches 
B) 12 inches 
C) 15 inches 
D) 8 inches 
E) 14 inches 
A) 16 inches 
B) 12 inches 
C) 15 inches 
D) 8 inches 
E) 14 inches

Question 18

Use the given zero to find the remaining zeros of the polynomial function below.

Accepted Answer

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

Question 19

Determine the domain of the rational function below.

Accepted Answer

A) all real numbers except 5 
B) all real numbers except -4 and 4 
C) all real numbers except 4 
D) all real numbers 
E) all real numbers except -5 and 5 
A) all real numbers except 5 
B) all real numbers except -4 and 4 
C) all real numbers except 4 
D) all real numbers 
E) all real numbers except -5 and 5

Use the Remainder Theorem to find for and .

Use translation and/or reflection concepts to explain how the graph of P can be used to produce the graph of Q .

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by where t is the number of months after the CD is released. Use S to predict the month in which sales are expected to reach a maximum.

Write as the product of and its reduced polynomial.

Find the real zeros of the polynomial function by factoring.

Use synthetic division to determine which of the following values of c is a zero of . 7, 7, 4, 3, 6

Find a polynomial function of lowest degree with integer coefficients that has the zeros 8, -1, -2.

A cylindrical soft drink can is to be made so that it will have a volume of 203 milliliters. If r is the radius of the can in centimeters, then the total surface area A of the can is given by the rational function . Does the graph of A have a slant asymptote?

Determine the vertical and slant asymptotes of the rational function below.

Find all the zeros of the polynomial function and write the polynomial as a product of its linear factors.

Find the zeros of the polynomial function . If a zero is a multiple zero, state its multiplicity.

Use the Rational Zero Theorem to list all possible rational zeros of the polynomial function .

Find a polynomial function P of degree 3 with integer coefficients that has zeros and .

Find a polynomial function of degree 4 with integer coefficients, whose leading coefficient is equal to one, and that has the zeros and .

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and the volume of the tank is cubic feet. Find, to the nearest thousandth of a foot, the length of the radius x.

A cube measures n inches on each edge. If a slice 5 inches thick is cut from one face of the cube, the resulting solid has a volume of 2250 cubic inches. Find n .

Use the given zero to find the remaining zeros of the polynomial function below.

Determine the domain of the rational function below.

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Exam 3: Polynomial and Rational Functions

Use the Remainder Theorem to find for and .

Use translation and/or reflection concepts to explain how the graph of P can be used to produce the graph of Q .

A music company expects that the monthly sales S , in thousands, of a new music CD it has produced will be closely approximated by where t is the number of months after the CD is released. Use S to predict the month in which sales are expected to reach a maximum.

Write as the product of and its reduced polynomial.

Find the real zeros of the polynomial function by factoring.

Use synthetic division to determine which of the following values of c is a zero of . 7, 7, 4, 3, 6

Find a polynomial function of lowest degree with integer coefficients that has the zeros 8, -1, -2.

A cylindrical soft drink can is to be made so that it will have a volume of 203 milliliters. If r is the radius of the can in centimeters, then the total surface area A of the can is given by the rational function . Does the graph of A have a slant asymptote?

Determine the vertical and slant asymptotes of the rational function below.

Find all the zeros of the polynomial function and write the polynomial as a product of its linear factors.

Find the zeros of the polynomial function . If a zero is a multiple zero, state its multiplicity.

Use the Rational Zero Theorem to list all possible rational zeros of the polynomial function .

Find a polynomial function P of degree 3 with integer coefficients that has zeros and .

Find a polynomial function of degree 4 with integer coefficients, whose leading coefficient is equal to one, and that has the zeros and .

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and the volume of the tank is cubic feet. Find, to the nearest thousandth of a foot, the length of the radius x.

A cube measures n inches on each edge. If a slice 5 inches thick is cut from one face of the cube, the resulting solid has a volume of 2250 cubic inches. Find n .

Use the given zero to find the remaining zeros of the polynomial function below.

Determine the domain of the rational function below.

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters