Question 1

Solve the inequality.
-$$\frac { x - 3 } { x + 7 } < 1$$

Accepted Answer

A)  $( - 7 , \infty )$ 
B)  $( - 7,3 )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - \infty , - 7 )$ or $( 3 , \infty )$ 
A)  $( - 7 , \infty )$ 
B)  $( - 7,3 )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - \infty , - 7 )$ or $( 3 , \infty )$

Question 2

Solve the inequality.
-$$x ^ { 3 } + 2 x ^ { 2 } - 63 x > 0$$

Accepted Answer

A)  $( - 9 , \infty )$ 
B)  $( - 9,0 )$ or $( 7 , \infty )$ 
C)  $( - \infty , - 9 )$ or $( 0,7 )$ 
D)  $( - 7,0 )$ or $( 9 , \infty )$ 
A)  $( - 9 , \infty )$ 
B)  $( - 9,0 )$ or $( 7 , \infty )$ 
C)  $( - \infty , - 9 )$ or $( 0,7 )$ 
D)  $( - 7,0 )$ or $( 9 , \infty )$

Question 3

Solve the inequality.
-$$2 x ^ { 2 } + 5 x < 3$$

Accepted Answer

A)  $( - \infty , - 3 )$ or $\left( \frac { 1 } { 2 } , \infty \right)$ 
B)  $( - 3 , \infty )$ 
C)  $\left( - 3 , \frac { 1 } { 2 } \right)$ 
D)  $\left( - \infty , \frac { 1 } { 2 } \right)$ 
A)  $( - \infty , - 3 )$ or $\left( \frac { 1 } { 2 } , \infty \right)$ 
B)  $( - 3 , \infty )$ 
C)  $\left( - 3 , \frac { 1 } { 2 } \right)$ 
D)  $\left( - \infty , \frac { 1 } { 2 } \right)$

Question 4

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 3 x ^ { 2 } + 3 x + 35$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 35 }$ 
B)  $\pm 1 , \pm 7 , \pm 5$ 
C)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 35 } , \pm 7 , \pm 5 , \pm 35$ 
D)  $\pm 1 , \pm 7 , \pm 5 , \pm 35$ 
A)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 35 }$ 
B)  $\pm 1 , \pm 7 , \pm 5$ 
C)  $\pm 1 , \pm \frac { 1 } { 7 } , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 35 } , \pm 7 , \pm 5 , \pm 35$ 
D)  $\pm 1 , \pm 7 , \pm 5 , \pm 35$

Question 5

Use the graph to find the vertical asymptotes, if any, of the function.
-

Accepted Answer

A)  $x = - 3 , x = 0$ 
B)  $x = - 3$ 
C)  $y = - 3$ 
D)  none 
A)  $x = - 3 , x = 0$ 
B)  $x = - 3$ 
C)  $y = - 3$ 
D)  none

Question 6

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

Accepted Answer

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

Question 7

Solve the inequality.
-$$x ^ { 3 } \geq 125$$

Accepted Answer

A)  $[ - 5,5 ]$ 
B)  $( - \infty , - 5 ]$ or $[ 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( - \infty , 5 ]$ 
A)  $[ - 5,5 ]$ 
B)  $( - \infty , - 5 ]$ or $[ 5 , \infty )$ 
C)  $[ 5 , \infty )$ 
D)  $( - \infty , 5 ]$

Question 8

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

Accepted Answer

A)  domain: $\{ x \mid x \neq 4 \}$
range: $\{ y \mid y \neq 2 \}$ 
B)  domain: $\{ x \mid x \neq 4 \}$
 range: $\{ y \mid y z - 2 \}$ 
C)  domain: $\{ x \mid x \neq 2 \}$
range: $\{ y \mid y \neq 4 \}$ 
D)  domain: $\{ x \mid x \neq - 2 \}$  
 range: $\{ y \mid y \neq 4 \}$ 
A)  domain: $\{ x \mid x \neq 4 \}$
range: $\{ y \mid y \neq 2 \}$ 
B)  domain: $\{ x \mid x \neq 4 \}$
 range: $\{ y \mid y z - 2 \}$ 
C)  domain: $\{ x \mid x \neq 2 \}$
range: $\{ y \mid y \neq 4 \}$ 
D)  domain: $\{ x \mid x \neq - 2 \}$  
 range: $\{ y \mid y \neq 4 \}$

Question 9

Solve the inequality.
-$$\frac { 14 } { x - 6 } > \frac { 12 } { x - 1 }$$

Accepted Answer

A)  $( - 29,1 )$ or $( 1,6 )$ 
B)  $( - 29,1 )$ or $( 6 , \infty )$ 
C)  $( - \infty , - 29 )$ or $( 1,6 )$ 
D)  $( - \infty , - 29 )$ or $( 6 , \infty )$ 
A)  $( - 29,1 )$ or $( 1,6 )$ 
B)  $( - 29,1 )$ or $( 6 , \infty )$ 
C)  $( - \infty , - 29 )$ or $( 1,6 )$ 
D)  $( - \infty , - 29 )$ or $( 6 , \infty )$

Question 10

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = \frac { 6 } { 5 } - \frac { 1 } { 5 } x$

Accepted Answer

A)  Yes; degree 0 
B)  Yes; degree 5 
C)  No; x has a fractional coefficient 
D)  Yes; degree 1 
A)  Yes; degree 0 
B)  Yes; degree 5 
C)  No; x has a fractional coefficient 
D)  Yes; degree 1

Question 11

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

Accepted Answer

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

Question 12

Find the vertical asymptotes of the rational function.
-$$h ( x ) = \frac { x + 4 } { x ^ { 2 } - 36 }$$

Accepted Answer

A)  $x = 36 , x = - 4$ 
B)  $x = - 6 , x = 6$ 
C)  $x = 0 , x = 36$ 
D)  $x = - 6 , x = 6 , x = - 4$ 
A)  $x = 36 , x = - 4$ 
B)  $x = - 6 , x = 6$ 
C)  $x = 0 , x = 36$ 
D)  $x = - 6 , x = 6 , x = - 4$

Question 13

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
-$$f ( x ) = - 2 ( x - 1 ) ( x + 3 ) ^ { 3 }$$

Accepted Answer

(a) For large values of @#LAT-DLM&, the graph of @#LAT-DLM&

Question 14

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).
-$$f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes; $f ( x ) = ( x - 5 ) \left( 2 x ^ { 2 } + 6 x - 9 \right)$ 
C)  Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + x + 9 \right)$ 
D)  Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + 6 x + 9 \right)$ 
A)  $\mathrm { No }$ 
B)  Yes; $f ( x ) = ( x - 5 ) \left( 2 x ^ { 2 } + 6 x - 9 \right)$ 
C)  Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + x + 9 \right)$ 
D)  Yes; $f ( x ) = ( x + 5 ) \left( 2 x ^ { 2 } + 6 x + 9 \right)$

Question 15

Find the x- and y-intercepts of f.
-$$f ( x ) = 3 x - x ^ { 3 }$$

Accepted Answer

A)  $x$-intercepts: $0 , - 3$; $y$-intercept: 0 
B)  $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 3 
C)  $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 0 
D)  x-intercepts: $0 , - 3 ; y$-intercept: 3 
A)  $x$-intercepts: $0 , - 3$; $y$-intercept: 0 
B)  $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 3 
C)  $x$-intercepts: $0 , \sqrt { 3 } , - \sqrt { 3 } ; y$-intercept: 0 
D)  x-intercepts: $0 , - 3 ; y$-intercept: 3

Question 16

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$3 x ^ { 3 } + 8 x ^ { 2 } - 15 x - 4 ; x + 4$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-The distance formula states that $\mathrm { d } = \mathrm { rt }$. If a car drives 50 miles, the function $\mathrm { r } = \frac { 50 } { \mathrm { t } }$ is a rational function. Find the asymptotes of this function.

Accepted Answer

horizontal asymptote

Question 18

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).
-$$f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$$

Accepted Answer

A)  Yes; $f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 19 x + 24 \right)$ 
B)  Yes; $f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x + 24 \right)$ 
C)  Yes; $f ( x ) = \left( x + \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x - 24 \right)$ 
D)  $\mathrm { No }$ 
A)  Yes; $f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 19 x + 24 \right)$ 
B)  Yes; $f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x + 24 \right)$ 
C)  Yes; $f ( x ) = \left( x + \frac { 1 } { 3 } \right) \left( 6 x ^ { 2 } + 18 x - 24 \right)$ 
D)  $\mathrm { No }$

Question 19

Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 8 x + 8$$

Accepted Answer

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

Question 20

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$$

Accepted Answer

A)  3 , multiplicity 1 , crosses $x$-axis; $- 7$, multiplicity 4 , touches $x$-axis 
B)  $- 3$, multiplicity 1 , touches $x$-axis; 7 , multiplicity 4 , crosses $x$-axis 
C)  $- 3$, multiplicity 1 , crosses $x$-axis; 7 , multiplicity 4 , touches $x$-axis 
D)  3 , multiplicity 1 , touches $x$-axis; $- 7$, multiplicity 4 , crosses $x$-axis 
A)  3 , multiplicity 1 , crosses $x$-axis; $- 7$, multiplicity 4 , touches $x$-axis 
B)  $- 3$, multiplicity 1 , touches $x$-axis; 7 , multiplicity 4 , crosses $x$-axis 
C)  $- 3$, multiplicity 1 , crosses $x$-axis; 7 , multiplicity 4 , touches $x$-axis 
D)  3 , multiplicity 1 , touches $x$-axis; $- 7$, multiplicity 4 , crosses $x$-axis

Solve the inequality. - $\frac { x - 3 } { x + 7 } < 1$

Solve the inequality. - $x ^ { 3 } + 2 x ^ { 2 } - 63 x > 0$

Solve the inequality. - $2 x ^ { 2 } + 5 x < 3$

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 3 x ^ { 2 } + 3 x + 35$

Use the graph to find the vertical asymptotes, if any, of the function. -

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

Solve the inequality. - $x ^ { 3 } \geq 125$

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

Solve the inequality. - $\frac { 14 } { x - 6 } > \frac { 12 } { x - 1 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { 6 } { 5 } - \frac { 1 } { 5 } x$

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

Find the vertical asymptotes of the rational function. - $h ( x ) = \frac { x + 4 } { x ^ { 2 } - 36 }$

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). - $f ( x ) = 2 x ^ { 3 } + 16 x ^ { 2 } + 39 x + 45 ; c = - 5$

Find the x- and y-intercepts of f. - $f ( x ) = 3 x - x ^ { 3 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $3 x ^ { 3 } + 8 x ^ { 2 } - 15 x - 4 ; x + 4$

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). - $f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 8 x + 8$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$

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

Solve the inequality. - x−3x+7<1\frac { x - 3 } { x + 7 } < 1x+7x−3​<1

Solve the inequality. - x3+2x2−63x>0x ^ { 3 } + 2 x ^ { 2 } - 63 x > 0x3+2x2−63x>0

Solve the inequality. - 2x2+5x<32 x ^ { 2 } + 5 x < 32x2+5x<3

List the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=x5−3x2+3x+35f ( x ) = x ^ { 5 } - 3 x ^ { 2 } + 3 x + 35f(x)=x5−3x2+3x+35