Question 1

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 2

Find the indicated intercept(s) of the graph of the function.2133:2139
-$3 x ^ { 3 } + 8 x ^ { 2 } - 15 x - 4 ; x + 4$

Accepted Answer

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

Question 3

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? A) $\{ x \mid 32 < x < 40 \}$

Accepted Answer

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

Question 4

Solve the inequality.
-$$\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0$$

Accepted Answer

A)  $( - \infty , - 3 )$ or $( 3 , \infty )$ 
B)  $( - \infty , - 3 )$ or $( 2,3 )$ 
C)  $( - 3,2 )$ or $( 3 , \infty )$ 
D)  $( - 3,2 )$ or $( 2,3 )$ 
A)  $( - \infty , - 3 )$ or $( 3 , \infty )$ 
B)  $( - \infty , - 3 )$ or $( 2,3 )$ 
C)  $( - 3,2 )$ or $( 3 , \infty )$ 
D)  $( - 3,2 )$ or $( 2,3 )$

Question 5

Find the indicated intercept(s) of the graph of the function.2133:2139
-$f ( x ) = 15 x ^ { 3 } + 49 x ^ { 2 } - 49 x - 99 ; x - \frac { 11 } { 3 }$

Accepted Answer

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

Question 6

Use the graph to determine the domain and range of the function.
-  A) domain: $\{ x \mid x \neq 4 \}$
range: $\{ y \mid y \neq 2 \}$

Accepted Answer

B)  domain: $\{ x \mid x \neq 4 \}$
range: $\{ y \mid y \neq - 2 \}$ 
C)  domain: $\{ x \mid x \neq 2 \}$
 range: $\{ y \mid y \neq 4 \}$ 
D)  domain: $\{ x \mid x \neq - 2 \}$   
range: $\{ y \mid y \neq 4 \}$ 
B)  domain: $\{ x \mid x \neq 4 \}$
range: $\{ y \mid y \neq - 2 \}$ 
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 7

Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } } { ( x + 4 ) ( x - 1 ) }$$

Accepted Answer

A)  $x = - 4 , x = 1 , x = - 2$ 
B)  $x = - 4 , x = 1$ 
C)  $x = - 2$ 
D)  $x = 4 , x = - 1$ 
A)  $x = - 4 , x = 1 , x = - 2$ 
B)  $x = - 4 , x = 1$ 
C)  $x = - 2$ 
D)  $x = 4 , x = - 1$

Question 8

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

Question 9

Solve the equation in the real number system.
-$$3 x ^ { 3 } - x ^ { 2 } + 3 x - 1 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } \right\}$
В) $\left\{ - 3 , - \frac { 1 } { 3 } , - 1 \right\}$ 
C)  $\left\{ \frac { 1 } { 3 } , - 1 \right\}$ 
D)  $\left\{ - 3 , \frac { 1 } { 3 } , - 1 \right\}$ 
A)  $\left\{ \frac { 1 } { 3 } \right\}$
В) $\left\{ - 3 , - \frac { 1 } { 3 } , - 1 \right\}$ 
C)  $\left\{ \frac { 1 } { 3 } , - 1 \right\}$ 
D)  $\left\{ - 3 , \frac { 1 } { 3 } , - 1 \right\}$

Question 10

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

Accepted Answer

A)  $\{ x \mid x \neq - 2 , x \neq 2 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq - 2 , x \neq 2 , x \neq - 4 \}$ 
D)  $\{ x \mid x \neq 0 , x \neq - 4 \}$ 
A)  $\{ x \mid x \neq - 2 , x \neq 2 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq - 2 , x \neq 2 , x \neq - 4 \}$ 
D)  $\{ x \mid x \neq 0 , x \neq - 4 \}$

Question 11

Use the graph to find the vertical asymptotes, if any, of the function.
-  A) $x = - 1 , x = 1 , y = 0$

Accepted Answer

B)  none 
C)  $x = - 1 , x = 1$ 
D)  $x = - 1 , x = 1 , x = 0$ 
B)  none 
C)  $x = - 1 , x = 1$ 
D)  $x = - 1 , x = 1 , x = 0$

Question 12

Find the indicated intercept(s) of the graph of the function.2133:2139
-$$x \text {-intercepts of } f ( x ) = \frac { x ^ { 2 } - 1 } { 2 + x ^ { 4 } }$$

Accepted Answer

A)  (1, 0) 
B)  (-1, 0), (1, 0) 
C)  (2, 0) 
D)  none 
A)  (1, 0) 
B)  (-1, 0), (1, 0) 
C)  (2, 0) 
D)  none

Question 13

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
-$$f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$$

Accepted Answer

A)  $- 4 , - 1,1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) ( x + 1 ) ( x + 4 )$ 
B)  $1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $4 , \frac { 3 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 3 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $- 4 , - 1,1 , - \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 3 ) ( x + 1 ) ( x + 4 )$ 
A)  $- 4 , - 1,1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) ( x + 1 ) ( x + 4 )$ 
B)  $1 , \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x - 3 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $4 , \frac { 3 } { 5 } ; f ( x ) = ( x - 4 ) ( 5 x - 3 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $- 4 , - 1,1 , - \frac { 3 } { 5 } ; f ( x ) = ( x - 1 ) ( 5 x + 3 ) ( x + 1 ) ( x + 4 )$

Question 14

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: -5, -3, 3; degree 3 A) $f ( x ) = x ^ { 3 } - 9 x - 5 x ^ { 2 } + 45$

Accepted Answer

B)  $f ( x ) = x ^ { 3 } + 9 x - 5 x ^ { 2 } - 45$ 
C)  $f ( x ) = x ^ { 3 } + 9 x + 5 x ^ { 2 } + 45$ 
D)  $f ( x ) = x ^ { 3 } - 9 x + 5 x ^ { 2 } - 45$ 
B)  $f ( x ) = x ^ { 3 } + 9 x - 5 x ^ { 2 } - 45$ 
C)  $f ( x ) = x ^ { 3 } + 9 x + 5 x ^ { 2 } + 45$ 
D)  $f ( x ) = x ^ { 3 } - 9 x + 5 x ^ { 2 } - 45$

Question 15

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 16

List the potential rational zeros of the polynomial function. Do not find the zeros.
-$$f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 6 x + 5$$

Accepted Answer

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

Question 17

Find the x- and y-intercepts of f.
-$$f ( x ) = 3 x - x ^ { 3 }$$ A) x-intercepts: $0 , - 3 ; y$-intercept: 0

Accepted Answer

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

Question 18

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 19

Solve the problem.
-$$( x - 2 ) ( x - 3 ) > 0$$

Accepted Answer

A)  $( 2,3 )$ 
B)  $( - \infty , 2 )$ 
C)  $( 3 , \infty )$ 
D)  $( - \infty , 2 )$ or $( 3 , \infty )$ 
A)  $( 2,3 )$ 
B)  $( - \infty , 2 )$ 
C)  $( 3 , \infty )$ 
D)  $( - \infty , 2 )$ or $( 3 , \infty )$

Question 20

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 2 x - 6 } { x - 4 }$$

Accepted Answer

A)  no oblique asymptotes 
B)  $x = y + 6$ 
C)  $y = x + 6$ 
D)  $y = x - 2$ 
A)  no oblique asymptotes 
B)  $x = y + 6$ 
C)  $y = x + 6$ 
D)  $y = x - 2$

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

Find the indicated intercept(s) of the graph of the function.2133:2139 - $3 x ^ { 3 } + 8 x ^ { 2 } - 15 x - 4 ; x + 4$

Solve the inequality. - $\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = 15 x ^ { 3 } + 49 x ^ { 2 } - 49 x - 99 ; x - \frac { 11 } { 3 }$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } } { ( x + 4 ) ( x - 1 ) }$

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

Solve the equation in the real number system. - $3 x ^ { 3 } - x ^ { 2 } + 3 x - 1 = 0$

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

Use the graph to find the vertical asymptotes, if any, of the function. - A) $x = - 1 , x = 1 , y = 0$ B) none C) $x = - 1 , x = 1$ D) $x = - 1 , x = 1 , x = 0$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x \text {-intercepts of } f ( x ) = \frac { x ^ { 2 } - 1 } { 2 + x ^ { 4 } }$

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. - $f ( x ) = 5 x ^ { 4 } - 8 x ^ { 3 } + 23 x ^ { 2 } - 32 x + 12$

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

List the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 5 x ^ { 2 } + 6 x + 5$

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

Solve the problem. - $( x - 2 ) ( x - 3 ) > 0$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 2 x - 6 } { x - 4 }$

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

Review

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Exam 3: Polynomial and Rational Functions

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 the indicated intercept(s) of the graph of the function.2133:2139 - 3x3+8x2−15x−4;x+43 x ^ { 3 } + 8 x ^ { 2 } - 15 x - 4 ; x + 43x3+8x2−15x−4;x+4

Solve the inequality. - (x−2)2x2−9>0\frac { ( x - 2 ) ^ { 2 } } { x ^ { 2 } - 9 } > 0x2−9(x−2)2​>0

Find the indicated intercept(s) of the graph of the function.2133:2139 - f(x)=15x3+49x2−49x−99;x−113f ( x ) = 15 x ^ { 3 } + 49 x ^ { 2 } - 49 x - 99 ; x - \frac { 11 } { 3 }f(x)=15x3+49x2−49x−99;x−311​

Find the vertical asymptotes of the rational function. - f(x)=2x2(x+4)(x−1)f ( x ) = \frac { 2 x ^ { 2 } } { ( x + 4 ) ( x - 1 ) }f(x)=(x+4)(x−1)2x2​