Question 1

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 horizontally 6 units to the left. 
B) Shift the graph of P vertically downward 6 units .. 
C) Shift the graph of P horizontally 6 units to the right. 
D) Shift the graph of P vertically upward 6 units . 
A) Shift the graph of P horizontally 6 units to the left. 
B) Shift the graph of P vertically downward 6 units .. 
C) Shift the graph of P horizontally 6 units to the right. 
D) Shift the graph of P vertically upward 6 units . C

Question 2

Use synthetic division to determine which of the following values of c is a zero of   .

Accepted Answer

A) -1 
B) -5 
C) -7 
D) -6 
E) -3 
A) -1 
B) -5 
C) -7 
D) -6 
E) -3 C

Question 3

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

Accepted Answer

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

Question 4

Sketch the graph of the polynomial function below.

Accepted Answer

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

Question 5

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by   where   . What is the maximum profit, to the nearest thousand dollars, the company can expect from the sale of its games?

Accepted Answer

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

Question 6

The rational function   models the number of milligrams of medication in the bloodstream of a patient t hours after 600 milligrams of the medication have been injected into the patient s bloodstream. Find   rounded to the nearest milligram.

Accepted Answer

A) 210 mg 
B) 180 mg 
C) 60 mg 
D) 10 mg 
E) 108 mg 
A) 210 mg 
B) 180 mg 
C) 60 mg 
D) 10 mg 
E) 108 mg

Question 7

The cost, in dollars, of producing x cellular telephones is given by   . The average cost per telephone is   . Use a graphing calculator to determine the minimum average cost per telephone, rounded to the nearest cent.

Accepted Answer

A) $4.61 
B) $37.00 
C) $28.00 
D) $20.08 
E) $109.00 
A) $4.61 
B) $37.00 
C) $28.00 
D) $20.08 
E) $109.00

Question 8

Use synthetic division to divide   by   .

Accepted Answer

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

Question 9

Use Descartes Rule of Signs to state the number of possible positive and negative real zeros of the polynomial function below.

Accepted Answer

A) three or one positive zeros; three or one negative zeros 
B) two or no positive zeros; four, two, or no negative zeros 
C) six, four, two, or no positive zeros; no negative zeros 
D) no positive zeros; six, four, two, or no negative zeros 
E) four, two, or no positive zeros; two or no negative zeros 
A) three or one positive zeros; three or one negative zeros 
B) two or no positive zeros; four, two, or no negative zeros 
C) six, four, two, or no positive zeros; no negative zeros 
D) no positive zeros; six, four, two, or no negative zeros 
E) four, two, or no positive zeros; two or no negative zeros

Question 10

Find all vertical asymptotes of the rational function   .

Accepted Answer

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

Question 11

A cylindrical soft drink can is to be made so that it will have a volume of 365 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   . Use the graph of A to estimate the value of r , to the nearest tenth of a centimeter, that will yield the minimum total surface area?

Accepted Answer

A) 7.1 cm 
B) 9.7 cm 
C) 19.4 cm 
D) 3.9 cm 
E) 3.1 cm 
A) 7.1 cm 
B) 9.7 cm 
C) 19.4 cm 
D) 3.9 cm 
E) 3.1 cm

Question 12

Use the Rational Zero Theorem to list possible rational zeros for the polynomial function below.

Accepted Answer

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

Question 13

Find the zeros of the polynomial function below and state the multiplicity of each zero.

Accepted Answer

A) 7 (multiplicity 1), -4 (multiplicity 2) 
B) 7 (multiplicity 2), -4 (multiplicity 1) 
C) -7 (multiplicity 1), 4 (multiplicity 2) 
D) -7 (multiplicity 2), 4 (multiplicity 1) 
E) 7 (multiplicity 2), 4 (multiplicity 1) 
A) 7 (multiplicity 1), -4 (multiplicity 2) 
B) 7 (multiplicity 2), -4 (multiplicity 1) 
C) -7 (multiplicity 1), 4 (multiplicity 2) 
D) -7 (multiplicity 2), 4 (multiplicity 1) 
E) 7 (multiplicity 2), 4 (multiplicity 1)

Question 14

The number of ways you can select three cards from a stack of n cards, in which the order of selection is important, is given by   . Use the Remainder Theorem to determine the number of ways you can select three cards from a stack of 9 cards.

Accepted Answer

A) 504 ways 
B) 336 ways 
C) 210 ways 
D) 120 ways 
E) 24 ways 
A) 504 ways 
B) 336 ways 
C) 210 ways 
D) 120 ways 
E) 24 ways

Question 15

The rational function   models the number of milligrams of medication in the bloodstream of a patient t hours after 350 milligrams of the medication have been injected into the patient s bloodstream. What will M approach as   ?

Accepted Answer

A) 12 mg 
B) 16 mg 
C) 8 mg 
D) 50 mg 
E) 0 mg 
A) 12 mg 
B) 16 mg 
C) 8 mg 
D) 50 mg 
E) 0 mg

Question 16

Determine the x -intercepts of the graph of   . For each x -intercept, use the Even and Odd Powers of   Theorem to determine whether the graph of P crosses the x -axis or intersects but does not cross the x -axis.

Accepted Answer

A) crosses the x -axis at   and   
B) crosses the x -axis at   ; intersects but does not cross at   
C) crosses the x -axis at   ; intersects but does not cross at   
D) crosses the x -axis at   ; intersects but does not cross at   
E) crosses the x -axis at   ; intersects but does not cross at   
A) crosses the x -axis at   and   
B) crosses the x -axis at   ; intersects but does not cross at   
C) crosses the x -axis at   ; intersects but does not cross at   
D) crosses the x -axis at   ; intersects but does not cross at   
E) crosses the x -axis at   ; intersects but does not cross at

Question 17

Find the horizontal asymptote of the rational function   .

Accepted Answer

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

Question 18

Use synthetic division and the Factor Theorem to determine whether or not   is a factor of   .

Accepted Answer

A) Yes,   a factor. 
B) No,   a factor. 
A) Yes,   a factor. 
B) No,   a factor.

Question 19

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is equal to 3, and that has the zeros   ,   and   .

Accepted Answer

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

Question 20

Determine the intercepts, vertical and horizontal asymptotes and sketch the graph of the rational function   .

Accepted Answer

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

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

Use synthetic division to determine which of the following values of c is a zero of .

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

Sketch the graph of the polynomial function below.

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by where . What is the maximum profit, to the nearest thousand dollars, the company can expect from the sale of its games?

The rational function models the number of milligrams of medication in the bloodstream of a patient t hours after 600 milligrams of the medication have been injected into the patient s bloodstream. Find rounded to the nearest milligram.

The cost, in dollars, of producing x cellular telephones is given by . The average cost per telephone is . Use a graphing calculator to determine the minimum average cost per telephone, rounded to the nearest cent.

Use synthetic division to divide by .

Use Descartes Rule of Signs to state the number of possible positive and negative real zeros of the polynomial function below.

Find all vertical asymptotes of the rational function .

Use the Rational Zero Theorem to list possible rational zeros for the polynomial function below.

Find the zeros of the polynomial function below and state the multiplicity of each zero.

The number of ways you can select three cards from a stack of n cards, in which the order of selection is important, is given by . Use the Remainder Theorem to determine the number of ways you can select three cards from a stack of 9 cards.

The rational function models the number of milligrams of medication in the bloodstream of a patient t hours after 350 milligrams of the medication have been injected into the patient s bloodstream. What will M approach as ?

Determine the x -intercepts of the graph of . For each x -intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x -axis or intersects but does not cross the x -axis.

Find the horizontal asymptote of the rational function .

Use synthetic division and the Factor Theorem to determine whether or not is a factor of .

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is equal to 3, and that has the zeros , and .

Determine the intercepts, vertical and horizontal asymptotes and sketch the graph of the rational function .

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

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Exam 3: Polynomial and Rational Functions

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

Use synthetic division to determine which of the following values of c is a zero of .

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

Sketch the graph of the polynomial function below.

A software company produces a computer game. The company has determined that its profit P , in dollars, from the manufacture and sale of x games is given by where . What is the maximum profit, to the nearest thousand dollars, the company can expect from the sale of its games?

The rational function models the number of milligrams of medication in the bloodstream of a patient t hours after 600 milligrams of the medication have been injected into the patient s bloodstream. Find rounded to the nearest milligram.

The cost, in dollars, of producing x cellular telephones is given by . The average cost per telephone is . Use a graphing calculator to determine the minimum average cost per telephone, rounded to the nearest cent.

Use synthetic division to divide by .

Use Descartes Rule of Signs to state the number of possible positive and negative real zeros of the polynomial function below.

Find all vertical asymptotes of the rational function .

Use the Rational Zero Theorem to list possible rational zeros for the polynomial function below.

Find the zeros of the polynomial function below and state the multiplicity of each zero.

The number of ways you can select three cards from a stack of n cards, in which the order of selection is important, is given by . Use the Remainder Theorem to determine the number of ways you can select three cards from a stack of 9 cards.

The rational function models the number of milligrams of medication in the bloodstream of a patient t hours after 350 milligrams of the medication have been injected into the patient s bloodstream. What will M approach as ?

Determine the x -intercepts of the graph of . For each x -intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x -axis or intersects but does not cross the x -axis.

Find the horizontal asymptote of the rational function .

Use synthetic division and the Factor Theorem to determine whether or not is a factor of .

Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is equal to 3, and that has the zeros , and .

Determine the intercepts, vertical and horizontal asymptotes and sketch the graph of the rational function .

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