Question 1

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 3 x ^ { 2 } + 2$$

Accepted Answer

A)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$ 
A)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$

Question 2

Graph the function using transformations.
-$$f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$$

Accepted Answer

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

Question 3

Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$$

Accepted Answer

A)  $f ( x ) = ( x + 3 i ) ( x - 3 i ) ( x + 4 i ) ( x - 4 i )$ 
B)  $f ( x ) = ( x + i ) ( x - i ) ( x + 12 i ) ( x - 12 i )$ 
C)  $f ( x ) = ( x + 3 i ) ^ { 2 } ( x + 4 i ) ^ { 2 }$ 
D)  $f ( x ) = ( x + 3 + 4 i ) ^ { 2 } ( x + 3 - 4 i ) ^ { 2 }$ 
A)  $f ( x ) = ( x + 3 i ) ( x - 3 i ) ( x + 4 i ) ( x - 4 i )$ 
B)  $f ( x ) = ( x + i ) ( x - i ) ( x + 12 i ) ( x - 12 i )$ 
C)  $f ( x ) = ( x + 3 i ) ^ { 2 } ( x + 4 i ) ^ { 2 }$ 
D)  $f ( x ) = ( x + 3 + 4 i ) ^ { 2 } ( x + 3 - 4 i ) ^ { 2 }$

Question 4

Give the equation of the oblique asymptote, if any, of the function.
-$$g ( x ) = \frac { x + 2 } { x ^ { 2 } - 25 }$$

Accepted Answer

A)  $y = 2 x$ 
B)  $y = 0$ 
C)  no oblique asymptote 
D)  $y = x + 2$ 
A)  $y = 2 x$ 
B)  $y = 0$ 
C)  no oblique asymptote 
D)  $y = x + 2$

Question 5

Choose the one alternative that best completes the statement or answers the question.
-Economists use what is called a Leffer curve to predict the government revenue for tax rates from $0 \%$ to $100 \%$. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces $t$ maximum revenue. Suppose an economist produces this rational function
$R ( x ) = \frac { 10 x ( 100 - x ) } { 25 + x }$, where $R$ is revenue in millions at a tax rate of $x$ percent. Use a graphing calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue?

Accepted Answer

A)  $38.4 \% ; \$ 383$ million 
B)  $27.0 \% ; \$ 379$ million 
C)  $28.8 \% ; \$ 272$ million 
D)  $30.9 \%$; $\$ 382$ million 
A)  $38.4 \% ; \$ 383$ million 
B)  $27.0 \% ; \$ 379$ million 
C)  $28.8 \% ; \$ 272$ million 
D)  $30.9 \%$; $\$ 382$ million

Question 6

Use transformations of the graph o to graph the function. $$y = x ^ { 4 } \text { or } y = x ^ { 5 }$$
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 5 }$$

Accepted Answer

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

Question 7

Find the indicated intercept(s) of the graph of the function.
-$y$-intercept of $f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }$

Accepted Answer

A)  $( 0,3 )$ 
B)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C)  $( 0,12 )$ 
D)  none 
A)  $( 0,3 )$ 
B)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C)  $( 0,12 )$ 
D)  none

Question 8

Write the word or phrase that best completes each statement or answers the question.
-The concentration C of a certain drug in a patient's bloodstream is given by $$\frac { 30 t } { t ^ { 2 } + 49 }$$ a) Find the horizontal asymptote of C(t).
b) Using a graphing utility, determine the time at which the concentration is highest.

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Solve the inequality.
-$$x ^ { 4 } < 81 x ^ { 2 }$$

Accepted Answer

A)  $( - \infty , - 9 )$ or $( 9 , \infty )$ 
B)  $( - 9,0 )$ or $( 9 , \infty )$ 
C)  $( - \infty , - 9 )$ or $( 0,9 )$ 
D)  $( - 9,0 )$ or $( 0,9 )$ 
A)  $( - \infty , - 9 )$ or $( 9 , \infty )$ 
B)  $( - 9,0 )$ or $( 9 , \infty )$ 
C)  $( - \infty , - 9 )$ or $( 0,9 )$ 
D)  $( - 9,0 )$ or $( 0,9 )$

Question 10

Determine the maximum number of turning points of f.
-$$f ( x ) = 9 x - x ^ { 3 }$$

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  1 
A)  2 
B)  3 
C)  4 
D)  1

Question 11

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = 5 x + 7 x ^ { 3 }$

Accepted Answer

A)  Yes; degree 7 
B)  Yes; degree 1 
C)  Yes; degree 3 
D)  Yes; degree 5 
A)  Yes; degree 7 
B)  Yes; degree 1 
C)  Yes; degree 3 
D)  Yes; degree 5

Question 12

Write the word or phrase that best completes each statement or answers the question.
-Which of the following functions could have this graph?

Accepted Answer

A)  $y = \frac { ( x + 1 ) ( x - 4 ) ^ { 2 } } { ( x - 2 ) 2 ( x - 6 ) }$ 
B)  $y = \frac { 2 ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 1 ) ( x - 4 ) ^ { 2 } }$ 
C)  $y = \frac { ( x - 2 ) ( x - 6 ) ^ { 2 } } { ( x + 1 ) 2 ( x - 4 ) }$ 
D)  $y = \frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 1 ) ( x - 4 ) ^ { 2 } }$ 
A)  $y = \frac { ( x + 1 ) ( x - 4 ) ^ { 2 } } { ( x - 2 ) 2 ( x - 6 ) }$ 
B)  $y = \frac { 2 ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 1 ) ( x - 4 ) ^ { 2 } }$ 
C)  $y = \frac { ( x - 2 ) ( x - 6 ) ^ { 2 } } { ( x + 1 ) 2 ( x - 4 ) }$ 
D)  $y = \frac { ( x - 2 ) ^ { 2 } ( x - 6 ) } { ( x + 1 ) ( x - 4 ) ^ { 2 } }$

Question 13

Find the domain of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$$

Accepted Answer

A)  all real numbers 
B)  $\{ x \mid x \neq - 3 , x \neq 5 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
D)  $\{ x \mid x \neq 3 , x \neq - 5 \}$ 
A)  all real numbers 
B)  $\{ x \mid x \neq - 3 , x \neq 5 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
D)  $\{ x \mid x \neq 3 , x \neq - 5 \}$

Question 14

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$$f ( x ) = x ^ { 5 } - 2.9 x ^ { 4 } - 13.51 x ^ { 3 } + 28.816 x ^ { 2 } + 37.76 x - 5.567$$

Accepted Answer

A)  5 ; 2 or 0 positive zeros; 2 or 0 negative zeros 
B)  $5 ; 2$ or 0 positive zeros; 3 or 1 negative zeros 
C)  5 ; 3 or 1 positive zeros; 3 or 1 negative zeros 
D)  5 ; 3 or 1 positive zeros; 2 or 0 negative zeros 
A)  5 ; 2 or 0 positive zeros; 2 or 0 negative zeros 
B)  $5 ; 2$ or 0 positive zeros; 3 or 1 negative zeros 
C)  5 ; 3 or 1 positive zeros; 3 or 1 negative zeros 
D)  5 ; 3 or 1 positive zeros; 2 or 0 negative zeros

Question 15

Graph the function using transformations.
-$$f ( x ) = \frac { 1 } { x } - 4$$

Accepted Answer

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

Question 16

Solve the inequality.
-$$\frac { ( x + 10 ) ( x - 2 ) } { x - 1 } \geq 0$$

Accepted Answer

A)  $( - \infty , - 10 ]$ or $[ 2 , \infty )$ 
B)  $[ - 10,1 )$ or $[ 2 , \infty )$ 
C)  $( - \infty , - 10 ]$ or $( 1,2 ]$ 
D)  $[ - 10,1 )$ or $( 1,2 ]$ 
A)  $( - \infty , - 10 ]$ or $[ 2 , \infty )$ 
B)  $[ - 10,1 )$ or $[ 2 , \infty )$ 
C)  $( - \infty , - 10 ]$ or $( 1,2 ]$ 
D)  $[ - 10,1 )$ or $( 1,2 ]$

Question 17

Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$$

Accepted Answer

A)  $f ( x ) = ( 3 x - 1 ) ( x - 2 ) ( x + 3 ) ( x - 3 )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )$ 
C)  $f ( x ) = ( 3 x - 1 ) ( x - 2 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x + 1 ) ( x + 2 ) ( x + 3 ) ( x - 3 )$ 
A)  $f ( x ) = ( 3 x - 1 ) ( x - 2 ) ( x + 3 ) ( x - 3 )$ 
B)  $f ( x ) = ( 3 x + 1 ) ( x + 2 ) ( x + 3 i ) ( x - 3 i )$ 
C)  $f ( x ) = ( 3 x - 1 ) ( x - 2 ) ( x + 3 i ) ( x - 3 i )$ 
D)  $f ( x ) = ( 3 x + 1 ) ( x + 2 ) ( x + 3 ) ( x - 3 )$

Question 18

Use the graph to find the oblique asymptote, if any, of the function.
-

Accepted Answer

A)  no oblique asymptote 
B)  $y = x + 2$ 
C)  $y = 3 x + 2$ 
D)  $y = 3$ 
A)  no oblique asymptote 
B)  $y = x + 2$ 
C)  $y = 3 x + 2$ 
D)  $y = 3$

Question 19

Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$630.00?

Accepted Answer

A)  $\{ x \mid 32 < x < 40 \}$ 
B)  $\{ x \mid 30 < x < 42 \}$ 
C)  $\{ \mathrm { x } \mid 39 < \mathrm { x } < 51 \}$ 
D)  $\{ x \mid 31 < x < 41 \}$ 
A)  $\{ x \mid 32 < x < 40 \}$ 
B)  $\{ x \mid 30 < x < 42 \}$ 
C)  $\{ \mathrm { x } \mid 39 < \mathrm { x } < 51 \}$ 
D)  $\{ x \mid 31 < x < 41 \}$

Question 20

Use the graph to find the horizontal asymptote, if any, of the function.
-

Accepted Answer

A)  $y = 6$ 
B)  none 
C)  $y = - 6$ 
D)  $y = 0$ 
A)  $y = 6$ 
B)  none 
C)  $y = - 6$ 
D)  $y = 0$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 3 x ^ { 2 } + 2$

Graph the function using transformations. - $f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$ $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$

Give the equation of the oblique asymptote, if any, of the function. - $g ( x ) = \frac { x + 2 } { x ^ { 2 } - 25 }$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = \frac { 1 } { 2 } x ^ { 5 }$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = \frac { 1 } { 2 } x ^ { 5 }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }$

Solve the inequality. - $x ^ { 4 } < 81 x ^ { 2 }$

Determine the maximum number of turning points of f. - $f ( x ) = 9 x - x ^ { 3 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 5 x + 7 x ^ { 3 }$

Write the word or phrase that best completes each statement or answers the question. -Which of the following functions could have this graph?

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 5 } - 2.9 x ^ { 4 } - 13.51 x ^ { 3 } + 28.816 x ^ { 2 } + 37.76 x - 5.567$

Graph the function using transformations. - $f ( x ) = \frac { 1 } { x } - 4$ $Graph the function using transformations. - f ( x ) = \frac { 1 } { x } - 4$

Solve the inequality. - $\frac { ( x + 10 ) ( x - 2 ) } { x - 1 } \geq 0$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$

Use the graph to find the oblique asymptote, if any, of the function. -

Solve the problem. -The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $630.00?

Use the graph to find the horizontal asymptote, if any, of the function. -

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 3: Polynomial and Rational Functions

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=6x4+4x3−3x2+2f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 3 x ^ { 2 } + 2f(x)=6x4+4x3−3x2+2

Graph the function using transformations. - f(x)=1x2+1f ( x ) = \frac { 1 } { x ^ { 2 } } + 1f(x)=x21​+1

Find all zeros of the function and write the polynomial as a product of linear factors. - f(x)=x4+25x2+144f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144f(x)=x4+25x2+144

Give the equation of the oblique asymptote, if any, of the function. - g(x)=x+2x2−25g ( x ) = \frac { x + 2 } { x ^ { 2 } - 25 }g(x)=x2−25x+2​

Use transformations of the graph o to graph the function. y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 - f(x)=12x5f ( x ) = \frac { 1 } { 2 } x ^ { 5 }f(x)=21​x5

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x2−12x2+2x−4f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }f(x)=x2+2x−4x2−12​

Solve the inequality. - x4<81x2x ^ { 4 } < 81 x ^ { 2 }x4<81x2

Determine the maximum number of turning points of f. - f(x)=9x−x3f ( x ) = 9 x - x ^ { 3 }f(x)=9x−x3

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=5x+7x3f ( x ) = 5 x + 7 x ^ { 3 }f(x)=5x+7x3

Write the word or phrase that best completes each statement or answers the question. -Which of the following functions could have this graph?

Find the domain of the rational function. - f(x)=2x2−43x2+6x−45f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }f(x)=3x2+6x−452x2−4​

Graph the function using transformations. - f(x)=1x−4f ( x ) = \frac { 1 } { x } - 4f(x)=x1​−4

Solve the inequality. - (x+10)(x−2)x−1≥0\frac { ( x + 10 ) ( x - 2 ) } { x - 1 } \geq 0x−1(x+10)(x−2)​≥0

Find all zeros of the function and write the polynomial as a product of linear factors. - f(x)=3x4−7x3+29x2−63x+18f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18f(x)=3x4−7x3+29x2−63x+18

Use the graph to find the oblique asymptote, if any, of the function. -

Solve the problem. -The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $14. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $630.00?

Use the graph to find the horizontal asymptote, if any, of the function. -

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = 6 x ^ { 4 } + 4 x ^ { 3 } - 3 x ^ { 2 } + 2$

Graph the function using transformations. - $f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$ $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$

Give the equation of the oblique asymptote, if any, of the function. - $g ( x ) = \frac { x + 2 } { x ^ { 2 } - 25 }$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = \frac { 1 } { 2 } x ^ { 5 }$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = \frac { 1 } { 2 } x ^ { 5 }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }$

Solve the inequality. - $x ^ { 4 } < 81 x ^ { 2 }$

Determine the maximum number of turning points of f. - $f ( x ) = 9 x - x ^ { 3 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 5 x + 7 x ^ { 3 }$

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Graph the function using transformations. - $f ( x ) = \frac { 1 } { x } - 4$ $Graph the function using transformations. - f ( x ) = \frac { 1 } { x } - 4$

Solve the inequality. - $\frac { ( x + 10 ) ( x - 2 ) } { x - 1 } \geq 0$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$