Question 1

Find a polynomial   of degree   that has the indicated zeros and satisfies the given condition.

Accepted Answer

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

Question 2

Find all values of   such that     .

Accepted Answer

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

Question 3

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft 2 .

Accepted Answer

A) 11 ft 
B) 13 ft 
C) 12 ft 
D) 10 ft 
E) 14 ft 
A) 11 ft 
B) 13 ft 
C) 12 ft 
D) 10 ft 
E) 14 ft C

Question 4

Find the domain   of   .

Accepted Answer

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

Question 5

Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 5%, approximately how much harder must the heart pump?

Accepted Answer

A) about 2.47 times as hard 
B) about 3.61 times as hard 
C) about 1.22 times as hard 
D) about 2.10 times as hard 
E) about 2.22 times as hard 
A) about 2.47 times as hard 
B) about 3.61 times as hard 
C) about 1.22 times as hard 
D) about 2.10 times as hard 
E) about 2.22 times as hard

Question 6

Use synthetic division to decide whether   is a zero of the equation.   ;

Accepted Answer

A) c is not a zero 
B) c is a zero 
A) c is not a zero 
B) c is a zero

Question 7

Find all solutions of the equation.

Accepted Answer

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

Question 8

Use the remainder theorem to find     ,

Accepted Answer

A) f ( 8 ) = 4,576 
B) f ( 8 ) = 4,620 
C) f ( 8 ) = 4,572 
D) f ( 8 ) = 4,580 
E) f ( 8 ) = 4,548 
A) f ( 8 ) = 4,576 
B) f ( 8 ) = 4,620 
C) f ( 8 ) = 4,572 
D) f ( 8 ) = 4,580 
E) f ( 8 ) = 4,548

Question 9

Find all values of   such that

Accepted Answer

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

Question 10

Find all solutions of the equation.

Accepted Answer

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

Question 11

Sketch the graph of   for the indicated value of   .

Accepted Answer

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

Question 12

Use the factor theorem to decide whether   is a factor of the polynomial.   ;

Accepted Answer

A) x - c is not a factor 
B) x - c is a factor 
A) x - c is not a factor 
B) x - c is a factor

Question 13

Find the fourth-degree polynomial function whose graph is shown in the figure.

Accepted Answer

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

Question 14

Use synthetic division to decide whether   is a zero of     ;

Accepted Answer

A) c is a zero of f ( x ) 
B) c is not a zero of f ( x ) 
A) c is a zero of f ( x ) 
B) c is not a zero of f ( x )

Question 15

Find all values of   such that     .

Accepted Answer

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

Question 16

Find an equation of a rational function   that satisfies the conditions. vertical asymptote: x = - 1, x = 0
Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1

Accepted Answer

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

Question 17

Sketch the graph of   .

Accepted Answer

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

Question 18

Find all solutions of the equation.

Accepted Answer

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

Question 19

Find all values of   such that

Accepted Answer

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

Question 20

Find the domain   of   .

Accepted Answer

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

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.

Find all values of such that .

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft².

Find the domain of .

Use synthetic division to decide whether is a zero of the equation. ;

Find all solutions of the equation.

Use the remainder theorem to find ,

Find all values of such that

Find all solutions of the equation.

Sketch the graph of for the indicated value of .

Use the factor theorem to decide whether is a factor of the polynomial. ;

Find the fourth-degree polynomial function whose graph is shown in the figure.

Use synthetic division to decide whether is a zero of ;

Find all values of such that .

Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 1, x = 0 Horizontal asymptote: y = 0 X-intercept: 8; f (9) = 1

Sketch the graph of .

Find all solutions of the equation.

Find all values of such that

Find the domain of .

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 4: Polynomial and Rational Functions

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.

Find all values of such that .

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft 2 .

Find the domain of .

Use synthetic division to decide whether is a zero of the equation. ;

Find all solutions of the equation.

Use the remainder theorem to find ,

Find all values of such that

Find all solutions of the equation.

Sketch the graph of for the indicated value of .

Use the factor theorem to decide whether is a factor of the polynomial. ;

Find the fourth-degree polynomial function whose graph is shown in the figure.

Use synthetic division to decide whether is a zero of ;

Find all values of such that .

Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 1, x = 0 Horizontal asymptote: y = 0 X-intercept: 8; f (9) = 1

Sketch the graph of .

Find all solutions of the equation.

Find all values of such that

Find the domain of .

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft².