Question 1

Describe the right-hand and the left-hand behavior of the graph of   .

Accepted Answer

A)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
A)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. A

Question 2

Write   in the form   when   .

Accepted Answer

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

Question 3

Write the standard form of the equation of the parabola that has a vertex at   and passes through the point   .

Accepted Answer

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

Question 4

Find a mathematical model for the verbal statement:

Accepted Answer

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

Question 5

Find all real solutions of the polynomial equation   .

Accepted Answer

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

Question 6

Hooke's law states that the magnitude of force, F, required to stretch a spring x units beyond its natural length is directly proportional to x. If a force of 2 pounds stretches a spring from its natural length of 10 inches to a length of 10.7 inches, what force will stretch the spring to a length of 11.5 inches? Round answer to nearest hundredth.

Accepted Answer

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

Question 7

Determine the x-intercept(s) of the quadratic function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  no x-intercept(s) 
A)    
B)    
C)    
D)    
E)  no x-intercept(s)

Question 8

Use the zero or root feature of a graphing utility to approximate the zeros of the function   accurate to the nearest thousandth.

Accepted Answer

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

Question 9

Find all real zeros of the polynomial   and determine the multiplicity of each.

Accepted Answer

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

Question 10

Use synthetic division to divide.

Accepted Answer

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

Question 11

Find all the real zeros of   .

Accepted Answer

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

Question 12

Use long division to divide.

Accepted Answer

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

Question 13

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of   .

Accepted Answer

A)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
B)  no positive reals; no negative reals 
C)  3 positive reals or 1 positive real; 1 negative real 
D)  1 positive real; 3 negative reals or 1 negative real 
E)  3 positive reals or 1 positive real; no negative reals 
A)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
B)  no positive reals; no negative reals 
C)  3 positive reals or 1 positive real; 1 negative real 
D)  1 positive real; 3 negative reals or 1 negative real 
E)  3 positive reals or 1 positive real; no negative reals

Question 14

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of   .

Accepted Answer

A)  1 positive real; 3 negative reals or 1 negative real 
B)  no positive reals; no negative reals 
C)  1 positive real; 5 negative reals or 3 negative reals or 1 negative real 
D)  5 positive reals or 3 positive reals or 1 positive real; no negative reals 
E)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
A)  1 positive real; 3 negative reals or 1 negative real 
B)  no positive reals; no negative reals 
C)  1 positive real; 5 negative reals or 3 negative reals or 1 negative real 
D)  5 positive reals or 3 positive reals or 1 positive real; no negative reals 
E)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 15

Write the quadratic function   in standard form.

Accepted Answer

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

Question 16

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of   .

Accepted Answer

A)  no positive reals; no negative reals 
B)  1 positive real; 3 negative reals or 1 negative real 
C)  0 positive real; 3 negative reals or 1 negative real 
D)  3 positive reals or 1 positive real; no negative reals 
E)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real 
A)  no positive reals; no negative reals 
B)  1 positive real; 3 negative reals or 1 negative real 
C)  0 positive real; 3 negative reals or 1 negative real 
D)  3 positive reals or 1 positive real; no negative reals 
E)  3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question 17

Use synthetic division to divide.

Accepted Answer

The answer of Use synthetic division to divide.  ...

Question 18

Find all zeros of the function   .

Accepted Answer

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

Question 19

Write the quadratic function   in standard form.

Accepted Answer

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

Question 20

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 280.

Accepted Answer

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

Describe the right-hand and the left-hand behavior of the graph of .

Write in the form when .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

Find a mathematical model for the verbal statement:

Find all real solutions of the polynomial equation .

Determine the x-intercept(s) of the quadratic function .

Use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to the nearest thousandth.

Find all real zeros of the polynomial and determine the multiplicity of each.

Use synthetic division to divide.

Find all the real zeros of .

Use long division to divide.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Write the quadratic function in standard form.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Use synthetic division to divide.

Find all zeros of the function .

Write the quadratic function in standard form.

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 280.

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 4: Polynomial Functions

Describe the right-hand and the left-hand behavior of the graph of .

Write in the form when .

Write the standard form of the equation of the parabola that has a vertex at and passes through the point .

Find a mathematical model for the verbal statement:

Find all real solutions of the polynomial equation .

Determine the x-intercept(s) of the quadratic function .

Use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to the nearest thousandth.

Find all real zeros of the polynomial and determine the multiplicity of each.

Use synthetic division to divide.

Find all the real zeros of .

Use long division to divide.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Write the quadratic function in standard form.

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of .

Use synthetic division to divide.

Find all zeros of the function .

Write the quadratic function in standard form.

Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 280.

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters