Question 1

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 1 ) ( x - 5 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts: $- 1,1,5$; y-intercept: 5 
B)  $x$-intercepts: $- 1,1,5$; y-intercept: $- 5$ 
C)  $x$-intercepts: $- 1,1 , - 5 ; y$-intercept: $- 5$ 
D)  $x$-intercepts: $- 1,1 , - 5$; $y$-intercept: 5 
A)  $x$-intercepts: $- 1,1,5$; y-intercept: 5 
B)  $x$-intercepts: $- 1,1,5$; y-intercept: $- 5$ 
C)  $x$-intercepts: $- 1,1 , - 5 ; y$-intercept: $- 5$ 
D)  $x$-intercepts: $- 1,1 , - 5$; $y$-intercept: 5

Question 2

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = ( x + 15 ) ^ { 2 }$$

Accepted Answer

A)  above the $x$-axis: $( - \infty , - 15 )$
below the $x$-axis: $( - 15 , \infty )$ 
B)  above the $x$-axis: $( - \infty , - 15 ) , ( - 15 , \infty )$ 
 below the $x$-axis: no intervals 
C)  above the x-axis: $( - 15 , \infty )$
below the $x$-axis: $( - \infty , - 15 )$ 
D)  above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , - 15 ) , ( - 15 , \infty )$ 
A)  above the $x$-axis: $( - \infty , - 15 )$
below the $x$-axis: $( - 15 , \infty )$ 
B)  above the $x$-axis: $( - \infty , - 15 ) , ( - 15 , \infty )$ 
 below the $x$-axis: no intervals 
C)  above the x-axis: $( - 15 , \infty )$
below the $x$-axis: $( - \infty , - 15 )$ 
D)  above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , - 15 ) , ( - 15 , \infty )$

Question 3

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c)(quotient).
-$$f ( x ) = x ^ { 6 } - 12 x ^ { 4 } - 69 x ^ { 2 } + 80 ; c = 4$$

Accepted Answer

A)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)$ 
B)  No 
C)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } - 4 x ^ { 3 } + 20 x ^ { 2 } - 5 x - 20 \right)$ 
D)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } + 4 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)$ 
A)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)$ 
B)  No 
C)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } - 4 x ^ { 3 } + 20 x ^ { 2 } - 5 x - 20 \right)$ 
D)  Yes; $f ( x ) = ( x - 4 ) \left( x ^ { 5 } + 4 x ^ { 4 } + 4 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 20 \right)$

Question 4

Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

A)  no horizontal asymptotes 
B)  $y = - 16$ 
C)  $y = 0$ 
D)  $y = - 1$ 
A)  no horizontal asymptotes 
B)  $y = - 16$ 
C)  $y = 0$ 
D)  $y = - 1$

Question 5

Graph the function.
-$$f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }$$

Accepted Answer

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

Question 6

Write the word or phrase that best completes each statement or answers the question.
The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places.
-$x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 = 0 ; - 3 \leq r \leq - 2$

Accepted Answer

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

Question 7

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: $- 4 , - 3 , - 1,5$; degree 4

Accepted Answer

A)  $x ^ { 4 } + 7 x ^ { 2 } - 60$ 
B)  $x ^ { 4 } - 3 x ^ { 3 } - 21 x ^ { 2 } + 83 x - 60$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 83 x - 60$ 
D)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 60 x - 60$ 
A)  $x ^ { 4 } + 7 x ^ { 2 } - 60$ 
B)  $x ^ { 4 } - 3 x ^ { 3 } - 21 x ^ { 2 } + 83 x - 60$ 
C)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 83 x - 60$ 
D)  $x ^ { 4 } + 3 x ^ { 3 } - 21 x ^ { 2 } - 60 x - 60$

Question 8

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$7 ( x - 1 ) ^ { 11 } ( x + 1 ) ^ { 3 }$

Accepted Answer

A)  Yes; degree 14 
B)  Yes; degree 11 
C)  Yes; degree 7 
D)  Yes; degree 77 
A)  Yes; degree 14 
B)  Yes; degree 11 
C)  Yes; degree 7 
D)  Yes; degree 77

Question 9

Use transformations of the graph o to graph the function. $$y = x ^ { 4 } \text { or } y = x ^ { 5 }$$
-$$f ( x ) = 3 - ( x - 4 ) ^ { 4 }$$

Accepted Answer

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

Question 10

Solve the inequality.
-$$( x + 2 ) ( x - 7 ) \leq 0$$

Accepted Answer

A)  $( - \infty , - 2 ]$ or $[ 7 , \infty )$ 
B)  $[ - 2,7 ]$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 7 , \infty )$ 
A)  $( - \infty , - 2 ]$ or $[ 7 , \infty )$ 
B)  $[ - 2,7 ]$ 
C)  $( - \infty , - 2 ]$ 
D)  $[ 7 , \infty )$

Question 11

Solve the inequality.
-$$\frac { x ^ { 2 } ( x - 11 ) ( x + 2 ) } { ( x - 4 ) ( x + 8 ) } \geq 0$$

Accepted Answer

A)  $( - 8 , - 2 ]$ or $( 4,11 ]$ 
B)  $( - \infty , - 8 )$ or $[ 11 , \infty )$ 
C)  $( - \infty , - 8 )$ or $[ - 2,0 )$ or $( 0,4 )$ or $[ 11 , \infty )$ 
D)  $( - \infty , - 8 )$ or $[ - 2,4 )$ or $[ 11 , \infty )$ 
A)  $( - 8 , - 2 ]$ or $( 4,11 ]$ 
B)  $( - \infty , - 8 )$ or $[ 11 , \infty )$ 
C)  $( - \infty , - 8 )$ or $[ - 2,0 )$ or $( 0,4 )$ or $[ 11 , \infty )$ 
D)  $( - \infty , - 8 )$ or $[ - 2,4 )$ or $[ 11 , \infty )$

Question 12

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.
-$$f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$$

Accepted Answer

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

Question 13

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]$$

Accepted Answer

A)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 2$; yes 
B)  $f ( - 1 ) = 3$ and $f ( 0 ) = 2$; no 
C)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 2$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 2$; no 
A)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 2$; yes 
B)  $f ( - 1 ) = 3$ and $f ( 0 ) = 2$; no 
C)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 2$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 2$; no

Question 14

Find the indicated intercept(s) of the graph of the function.
-$y$-intercept of $f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 10 x - 13 }$

Accepted Answer

A)  $( 0,0 )$ 
B)  $\left( 0 , - \frac { 13 } { 5 } \right)$ 
C)  $\left( 0 , \frac { 5 } { 13 } \right)$ 
D)  $( 0,5 )$ 
A)  $( 0,0 )$ 
B)  $\left( 0 , - \frac { 13 } { 5 } \right)$ 
C)  $\left( 0 , \frac { 5 } { 13 } \right)$ 
D)  $( 0,5 )$

Question 15

Find the indicated intercept(s) of the graph of the function.
-$y$-intercept of $f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 0,3 )$ 
C)  $\left( 0 , - \frac { 1 } { 60 } \right)$ 
D)  none 
A)  $( 0,0 )$ 
B)  $( 0,3 )$ 
C)  $\left( 0 , - \frac { 1 } { 60 } \right)$ 
D)  none

Question 16

Find the domain of the rational function.
-$$R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }$$

Accepted Answer

A)  $\{ x | x \neq - 7,5 \rangle$ 
B)  $\{ x | x \neq 7,5 \rangle$ 
C)  $\{ x | x \neq - 35,1 \rangle$ 
D)  $\{ x | x \neq 7 , - 5 \rangle$ 
A)  $\{ x | x \neq - 7,5 \rangle$ 
B)  $\{ x | x \neq 7,5 \rangle$ 
C)  $\{ x | x \neq - 35,1 \rangle$ 
D)  $\{ x | x \neq 7 , - 5 \rangle$

Question 17

Solve the problem.
-Decide which of the rational functions might have the given graph.

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 2 x }$ 
B)  $f ( x ) = x ^ { 2 }$ 
C)  $f ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } }$ 
A)  $f ( x ) = \frac { 1 } { 2 x }$ 
B)  $f ( x ) = x ^ { 2 }$ 
C)  $f ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } }$

Question 18

Find the domain of the rational function.
-$$h ( x ) = \frac { 8 x } { x - 5 }$$

Accepted Answer

A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq - 5 \}$ 
C)  $\{ x \mid x \neq 5 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq - 5 \}$ 
C)  $\{ x \mid x \neq 5 \}$ 
D)  all real numbers

Question 19

Use the graph to determine the domain and range of the function.
-

Accepted Answer

A)  domain: $\{ x \mid x \leq 0$ or $x > 1 \}$
 range: $\{ y \mid y \neq - 2 , y \neq 2 \}$ 
B)  domain: all real numbers 
range: all real numbers 
C)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$
range: $\{ y \mid y \leq 0$ or $y \geq 1 \}$ 
D)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$  
range: $\{ y \mid y \leq 0$ or $y > 1 \}$ 
A)  domain: $\{ x \mid x \leq 0$ or $x > 1 \}$
 range: $\{ y \mid y \neq - 2 , y \neq 2 \}$ 
B)  domain: all real numbers 
range: all real numbers 
C)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$
range: $\{ y \mid y \leq 0$ or $y \geq 1 \}$ 
D)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$  
range: $\{ y \mid y \leq 0$ or $y > 1 \}$

Question 20

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: 0, - 7, 6; degree 3

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x - 42$ 
B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$ 
C)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$ 
A)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x - 42$ 
B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$ 
C)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 5 ) ( x - 1 ) ^ { 2 }$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x + 15 ) ^ { 2 }$

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). - $f ( x ) = x ^ { 6 } - 12 x ^ { 4 } - 69 x ^ { 2 } + 80 ; c = 4$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }$

Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - $x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 = 0 ; - 3 \leq r \leq - 2$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 4 , - 3 , - 1,5$ ; degree 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $7 ( x - 1 ) ^ { 11 } ( x + 1 ) ^ { 3 }$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = 3 - ( x - 4 ) ^ { 4 }$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = 3 - ( x - 4 ) ^ { 4 }$

Solve the inequality. - $( x + 2 ) ( x - 7 ) \leq 0$

Solve the inequality. - $\frac { x ^ { 2 } ( x - 11 ) ( x + 2 ) } { ( x - 4 ) ( x + 8 ) } \geq 0$

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. - $f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 10 x - 13 }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }$

Find the domain of the rational function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }$

Solve the problem. -Decide which of the rational functions might have the given graph.

Find the domain of the rational function. - $h ( x ) = \frac { 8 x } { x - 5 }$

Use the graph to determine the domain and range of the function. -

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: 0, - 7, 6; degree 3

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

Find the x- and y-intercepts of f. - f(x)=(x+1)(x−5)(x−1)2f ( x ) = ( x + 1 ) ( x - 5 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−5)(x−1)2

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - f(x)=(x+15)2f ( x ) = ( x + 15 ) ^ { 2 }f(x)=(x+15)2

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). - f(x)=x6−12x4−69x2+80;c=4f ( x ) = x ^ { 6 } - 12 x ^ { 4 } - 69 x ^ { 2 } + 80 ; c = 4f(x)=x6−12x4−69x2+80;c=4

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=−x2+16x2+5x+4f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }f(x)=x2+5x+4−x2+16​

Graph the function. - f(x)=x2−4x+4x2−3f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }f(x)=x2−3x2−4x+4​

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: −4,−3,−1,5- 4 , - 3 , - 1,5−4,−3,−1,5 ; degree 4

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - 7(x−1)11(x+1)37 ( x - 1 ) ^ { 11 } ( x + 1 ) ^ { 3 }7(x−1)11(x+1)3

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)=3−(x−4)4f ( x ) = 3 - ( x - 4 ) ^ { 4 }f(x)=3−(x−4)4

Solve the inequality. - (x+2)(x−7)≤0( x + 2 ) ( x - 7 ) \leq 0(x+2)(x−7)≤0

Solve the inequality. - x2(x−11)(x+2)(x−4)(x+8)≥0\frac { x ^ { 2 } ( x - 11 ) ( x + 2 ) } { ( x - 4 ) ( x + 8 ) } \geq 0(x−4)(x+8)x2(x−11)(x+2)​≥0

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)=−2x5+x3−x2+3f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3f(x)=−2x5+x3−x2+3

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=7x3−2x+2;[−1,0]f ( x ) = 7 x ^ { 3 } - 2 x + 2 ; [ - 1,0 ]f(x)=7x3−2x+2;[−1,0]

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x2−5xx2+10x−13f ( x ) = \frac { x ^ { 2 } - 5 x } { x ^ { 2 } + 10 x - 13 }f(x)=x2+10x−13x2−5x​

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x(x+20)(x−3)f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }f(x)=(x+20)(x−3)x​

Find the domain of the rational function. - R(x)=−3x2x2+2x−35R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 2 x - 35 }R(x)=x2+2x−35−3x2​