Question 1

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$$

Accepted Answer

A) True 
 B)False  True

Question 2

Translate the given formula to an English phrase using the word "varies".
-If y varies directly as x, and x is doubled, how is y changed?

Accepted Answer

A)  y is unchanged 
B)  y is increased by 2 
C)  y is doubled 
D)  y is halved 
A)  y is unchanged 
B)  y is increased by 2 
C)  y is doubled 
D)  y is halved C

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$2 x ^ { 2 } + 9 x < 35$$

Accepted Answer

A)  $\left( - 7 , \frac { 5 } { 2 } \right)$ 
B)  $\left( \infty , - \frac { 5 } { 2 } \right) \cup ( 7 , \infty )$ 
C)  $( \infty , - 7 ) \cup \left( \frac { 5 } { 2 } , \infty \right)$ 
D)  $\left( - \frac { 5 } { 2 } , 7 \right)$ 
A)  $\left( - 7 , \frac { 5 } { 2 } \right)$ 
B)  $\left( \infty , - \frac { 5 } { 2 } \right) \cup ( 7 , \infty )$ 
C)  $( \infty , - 7 ) \cup \left( \frac { 5 } { 2 } , \infty \right)$ 
D)  $\left( - \frac { 5 } { 2 } , 7 \right)$ A

Question 4

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
-$$f ( x ) = 6 x ^ { 3 } - 8 x ^ { 2 } + 8 x + 5$$

Accepted Answer

A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 & 2 & 0 \
0 & 2 & 1
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 0 & 2 & 1 \
0 & 1 & 2
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 &1 & 1 \
0 & 0 & 3
\end{array}$ 
D)  
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 1 & 0 \
0 & 1 & 2
\end{array}$ 
A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 & 2 & 0 \
0 & 2 & 1
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 0 & 2 & 1 \
0 & 1 & 2
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 &1 & 1 \
0 & 0 & 3
\end{array}$ 
D)  
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 1 & 0 \
0 & 1 & 2
\end{array}$

Question 5

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
B)  $P ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
C)  $P ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$ 
D)  $P ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$ 
A)  $P ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
B)  $P ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
C)  $P ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$ 
D)  $P ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$

Question 6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$k = - 2 ; f ( x ) = 4 x ^ { 3 } + 9 x ^ { 2 } + x - 2$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 7

Find all rational zeros and factor f(x).
-$$f ( x ) = 10 x ^ { 3 } + 43 x ^ { 2 } + 11 x - 4$$

Accepted Answer

A)  $- 2,5 , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$ 
B)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$ 
C)  $- 2,5 , - 4 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 4 )$ 
D)  $- \frac { 1 } { 10 } , 1 , - 4 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 4 )$ 
A)  $- 2,5 , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$ 
B)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 4 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 4 )$ 
C)  $- 2,5 , - 4 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 4 )$ 
D)  $- \frac { 1 } { 10 } , 1 , - 4 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 4 )$

Question 8

Find the equation that the given graph represents.
-$$f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 3 }$$

Accepted Answer

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

Question 9

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = - 7 x ^ { 4 } - 9 x ^ { 3 } - 4 x - 5 ; - 1$ and 0

Accepted Answer

A)  $f ( - 1 ) = - 1$ and $f ( 0 ) = 5$ 
B)  $f ( - 1 ) = 1$ and $f ( 0 ) = - 5$ 
C)  $f ( - 1 ) = - 1$ and $f ( 0 ) = - 5$ 
D)  $f ( - 1 ) = 2$ and $f ( 0 ) = - 4$ 
A)  $f ( - 1 ) = - 1$ and $f ( 0 ) = 5$ 
B)  $f ( - 1 ) = 1$ and $f ( 0 ) = - 5$ 
C)  $f ( - 1 ) = - 1$ and $f ( 0 ) = - 5$ 
D)  $f ( - 1 ) = 2$ and $f ( 0 ) = - 4$

Question 10

Solve the problem
-John owns a hotdog stand. His profit is represented by the equation $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 12 \mathrm { x } + 45$, with $\mathrm { P }$ being profits and $x$ the number of hotdogs sold. What is the most he can earn?

Accepted Answer

A)  $81 
B)  $117 
C)  $63 
D)  $36 
A)  $81 
B)  $117 
C)  $63 
D)  $36

Question 11

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
-$$f ( x ) = 3 x ^ { 5 } - 7 x ^ { 4 } + 3 x ^ { 3 } - 7$$

Accepted Answer

A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 1 \
2 & 0 & 3 \
0 & 0 & 5
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 3 & 1 & 1 \
1 & 3 & 1 \
1 & 1 & 3
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 & 3 & 1 \
1 & 1 & 3 \

\end{array}$ 
D) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 3 & 0 & 2 \
1 & 0 & 4 \
\end{array}$ 
A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 1 \
2 & 0 & 3 \
0 & 0 & 5
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 3 & 1 & 1 \
1 & 3 & 1 \
1 & 1 & 3
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 1 & 3 & 1 \
1 & 1 & 3 \

\end{array}$ 
D) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 3 & 0 & 2 \
1 & 0 & 4 \
\end{array}$

Question 12

Solve the problem
-A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production. $$\begin{array} { c | c c c c c } 
\text { Number of } & & & & & \
\text { Desks Produced } & 120 & 350 & 500 & 650 & 750 \
\hline \text { Profit (Thousands) } & 13 & 37 & 44 & 34 & 25
\end{array}$$ Find a quadratic function to model the data, and use the model to predict the profit if 450 chairs are made.
Round to the nearest thousand.

Accepted Answer

A)  $44,000 
B)  $40,000 
C)  $42,000 
D)  $45,000 
A)  $44,000 
B)  $40,000 
C)  $42,000 
D)  $45,000

Question 13

Round your answer to two decimal places.
-The weight of a body above the surface of the earth is inversely proportional to the square of its 489) distance from the center of the earth. What is the effect on the weight when the distance is
Multiplied by 2?

Accepted Answer

A)  The weight is multiplied by 2. 
B)  The weight is divided by 2. 
C)  The weight is multiplied by 4. 
D)  The weight is divided by 4. 
A)  The weight is multiplied by 2. 
B)  The weight is divided by 2. 
C)  The weight is multiplied by 4. 
D)  The weight is divided by 4.

Question 14

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } - 18 x + 83$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $[ 9 , \infty )$ 
B)  Domain: $[ 2 , \infty )$; Range: $( - \infty , 9 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 2 , \infty )$ 
D)  Domain: $[ 2 , \infty )$; Range: $( - \infty , 0 ]$ 
A)  Domain: $( - \infty , \infty )$; Range: $[ 9 , \infty )$ 
B)  Domain: $[ 2 , \infty )$; Range: $( - \infty , 9 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 2 , \infty )$ 
D)  Domain: $[ 2 , \infty )$; Range: $( - \infty , 0 ]$

Question 15

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; - 2 i$$

Accepted Answer

A)  $2 i , 6 , - 6$ 
B)  $2 \mathrm { i } , 12 , - 12$ 
C)  $2 i , 6 i , - 6 i$ 
D)  $2 \mathrm { i } , 12 \mathrm { i } , - 12 \mathrm { i }$ 
A)  $2 i , 6 , - 6$ 
B)  $2 \mathrm { i } , 12 , - 12$ 
C)  $2 i , 6 i , - 6 i$ 
D)  $2 \mathrm { i } , 12 \mathrm { i } , - 12 \mathrm { i }$

Question 16

Find the domain and range of the function.
-$$f ( x ) = x ^ { 2 } + 4 x + 1$$

Accepted Answer

A)  Domain: $[ - 3 , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 3 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ - 2 , \infty )$ 
D)  Domain: $[ - 3 , \infty )$; Range: $( - \infty , - 2 ]$ 
A)  Domain: $[ - 3 , \infty )$; Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 3 , \infty )$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ - 2 , \infty )$ 
D)  Domain: $[ - 3 , \infty )$; Range: $( - \infty , - 2 ]$

Question 17

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$2 x ^ { 2 } - 2 x + 60 ; x - 5$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 18

Factor f(x) into linear factors given that k is a zero of f(x).
-$f ( x ) = x ^ { 3 } - ( 4 + 2 i ) x ^ { 2 } + ( - 5 + 8 i ) x + 10 i ; k = 2 i$

Accepted Answer

A)  $f ( x ) = ( x - i ) ( x + 1 ) ( x - 10 )$ 
B)  $f ( x ) = ( x - 2 i ) ( x - 1 ) ( x + 5 )$ 
C)  $f ( x ) = ( x + 2 i ) ( x - 1 ) ( x - 5 )$ 
D)  $f ( x ) = ( x - 2 i ) ( x + 1 ) ( x - 5 )$ 
A)  $f ( x ) = ( x - i ) ( x + 1 ) ( x - 10 )$ 
B)  $f ( x ) = ( x - 2 i ) ( x - 1 ) ( x + 5 )$ 
C)  $f ( x ) = ( x + 2 i ) ( x - 1 ) ( x - 5 )$ 
D)  $f ( x ) = ( x - 2 i ) ( x + 1 ) ( x - 5 )$

Question 19

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $1 , - 2,3$ and $\mathrm { P } ( 2 ) = 20$

Accepted Answer

A)  $P ( x ) = - 5 x ^ { 3 } - 20 x ^ { 2 } + 25 x - 30$ 
B)  $P ( x ) = 5 x ^ { 3 } + 20 x ^ { 2 } - 25 x + 30$ 
C)  $P ( x ) = 5 x ^ { 3 } - 10 x ^ { 2 } - 25 x + 30$ 
D)  $P ( x ) = - 5 x ^ { 3 } + 10 x ^ { 2 } + 25 x - 30$ 
A)  $P ( x ) = - 5 x ^ { 3 } - 20 x ^ { 2 } + 25 x - 30$ 
B)  $P ( x ) = 5 x ^ { 3 } + 20 x ^ { 2 } - 25 x + 30$ 
C)  $P ( x ) = 5 x ^ { 3 } - 10 x ^ { 2 } - 25 x + 30$ 
D)  $P ( x ) = - 5 x ^ { 3 } + 10 x ^ { 2 } + 25 x - 30$

Question 20

Determine whether the statement is true or false.
-If f(x) is a polynomial and f(3) = 0, then x + 3 is a factor of f(x).

Accepted Answer

A) True 
 B)False

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$

Translate the given formula to an English phrase using the word "varies". -If y varies directly as x, and x is doubled, how is y changed?

Solve the inequality. Write the solution set in interval notation. - $2 x ^ { 2 } + 9 x < 35$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $f ( x ) = 6 x ^ { 3 } - 8 x ^ { 2 } + 8 x + 5$

Find the equation that the given graph represents. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 2 ; f ( x ) = 4 x ^ { 3 } + 9 x ^ { 2 } + x - 2$

Find all rational zeros and factor f(x). - $f ( x ) = 10 x ^ { 3 } + 43 x ^ { 2 } + 11 x - 4$

Find the equation that the given graph represents. - $f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 3 }$ $Find the equation that the given graph represents. - f ( x ) = \frac { 1 } { 4 } ( x - 4 ) ^ { 3 }$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = - 7 x ^ { 4 } - 9 x ^ { 3 } - 4 x - 5 ; - 1$ and 0

Solve the problem -John owns a hotdog stand. His profit is represented by the equation $\mathrm { P } ( \mathrm { x } ) = - \mathrm { x } ^ { 2 } + 12 \mathrm { x } + 45$ , with $\mathrm { P }$ being profits and $x$ the number of hotdogs sold. What is the most he can earn?

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $f ( x ) = 3 x ^ { 5 } - 7 x ^ { 4 } + 3 x ^ { 3 } - 7$

Round your answer to two decimal places. -The weight of a body above the surface of the earth is inversely proportional to the square of its 489) distance from the center of the earth. What is the effect on the weight when the distance is Multiplied by 2?

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } - 18 x + 83$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; - 2 i$

Find the domain and range of the function. - $f ( x ) = x ^ { 2 } + 4 x + 1$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $2 x ^ { 2 } - 2 x + 60 ; x - 5$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - ( 4 + 2 i ) x ^ { 2 } + ( - 5 + 8 i ) x + 10 i ; k = 2 i$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $1 , - 2,3$ and $\mathrm { P } ( 2 ) = 20$

Determine whether the statement is true or false. -If f(x) is a polynomial and f(3) = 0, then x + 3 is a factor of f(x).

Review of Basic Concepts

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

Filters

Exam 4: Polynomial and Rational Functions

Determine whether the statement is true or false. - The function f(x)=3x is an odd function. \text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. } The function f(x)=x3​ is an odd function.

Translate the given formula to an English phrase using the word "varies". -If y varies directly as x, and x is doubled, how is y changed?

Solve the inequality. Write the solution set in interval notation. - 2x2+9x<352 x ^ { 2 } + 9 x < 352x2+9x<35

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - f(x)=6x3−8x2+8x+5f ( x ) = 6 x ^ { 3 } - 8 x ^ { 2 } + 8 x + 5f(x)=6x3−8x2+8x+5