Question 1

Solve the inequality.
-$$\frac { x + 25 } { x + 4 } < 9$$

Accepted Answer

A)  $( - \infty , - 4 )$ or $\left( - \frac { 11 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 11 } { 8 } \right)$ or $( 4 , \infty )$ 
C)  $( - \infty , - 4 )$ or $( 4 , \infty )$ 
D)  $\left( - 4 , - \frac { 11 } { 8 } \right)$ 
A)  $( - \infty , - 4 )$ or $\left( - \frac { 11 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 11 } { 8 } \right)$ or $( 4 , \infty )$ 
C)  $( - \infty , - 4 )$ or $( 4 , \infty )$ 
D)  $\left( - 4 , - \frac { 11 } { 8 } \right)$

Question 2

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function.
-$$f ( x ) = \frac { 1 } { 2 } ( x + 4 ) ^ { 4 } + 3$$
 
 A)

Accepted Answer

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

Question 3

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

Accepted Answer

A)  y = 5 
B)  x = 2, y = 5 
C)  x = 3, x = 0 
D)  x = 3 
A)  y = 5 
B)  x = 2, y = 5 
C)  x = 3, x = 0 
D)  x = 3

Question 4

Solve the inequality.
-$$\frac { 15 x } { 5 - x } \geq 5 x$$

Accepted Answer

A)  $[ 5 , \infty )$ 
B)  $( - \infty , 0 ]$ or $[ 2,5 )$ 
C)  $( - \infty , 2 ]$ or $[ 5 , \infty )$ 
D)  $[ 0,2 ]$ or $[ 5 , \infty )$ 
A)  $[ 5 , \infty )$ 
B)  $( - \infty , 0 ]$ or $[ 2,5 )$ 
C)  $( - \infty , 2 ]$ or $[ 5 , \infty )$ 
D)  $[ 0,2 ]$ or $[ 5 , \infty )$

Question 5

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

Accepted Answer

A)  x-intercepts: 0, 1, 5; y-intercept: 0 
B)  x-intercepts: 0, 1, 5; y-intercept: 5 
C)  x-intercepts: 0, -1, -5; y-intercept: 5 
D)  x-intercepts: 0, -1, -5; y-intercept: 0 
A)  x-intercepts: 0, 1, 5; y-intercept: 0 
B)  x-intercepts: 0, 1, 5; y-intercept: 5 
C)  x-intercepts: 0, -1, -5; y-intercept: 5 
D)  x-intercepts: 0, -1, -5; y-intercept: 0

Question 6

Find the indicated intercept(s) of the graph of the function.2133:2139
-$y$-intercept of $f ( x ) = \frac { x ^ { 2 } - 15 x + 6 } { 2 x }$

Accepted Answer

A)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
B)  $( 0,6 )$ 
C)  $( 0,3 )$ 
D)  none 
A)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
B)  $( 0,6 )$ 
C)  $( 0,3 )$ 
D)  none

Question 7

Find the domain of the rational function.
-$$f ( x ) = \frac { - 2 x ( x + 2 ) } { 5 x ^ { 2 } - 3 x - 8 }$$

Accepted Answer

A)  $\left\{ x \mid x \neq - \frac { 5 } { 8 } , 1 \right\}$ 
B)  $\left\{ x \mid x \neq \frac { 5 } { 8 } , - 1 \right\}$ 
C)  $\left\{ x \mid x \neq - \frac { 8 } { 5 } , 1 \right\}$ 
D)  $\left\{ x \mid x \neq \frac { 8 } { 5 } , - 1 \right\}$ 
A)  $\left\{ x \mid x \neq - \frac { 5 } { 8 } , 1 \right\}$ 
B)  $\left\{ x \mid x \neq \frac { 5 } { 8 } , - 1 \right\}$ 
C)  $\left\{ x \mid x \neq - \frac { 8 } { 5 } , 1 \right\}$ 
D)  $\left\{ x \mid x \neq \frac { 8 } { 5 } , - 1 \right\}$

Question 8

Find the indicated intercept(s) of the graph of the function.2133:2139
-$x$-intercepts of $f ( x ) = \frac { ( x - 8 ) ( 2 x + 7 ) } { x ^ { 2 } + 3 x - 4 }$

Accepted Answer

A)  $( - 8,0 ) , \left( \frac { 7 } { 2 } , 0 \right)$ 
B)  $( 8,0 ) , ( - 7,0 )$ 
C)  $( 8,0 ) , \left( - \frac { 7 } { 2 } , 0 \right)$ 
D)  none 
A)  $( - 8,0 ) , \left( \frac { 7 } { 2 } , 0 \right)$ 
B)  $( 8,0 ) , ( - 7,0 )$ 
C)  $( 8,0 ) , \left( - \frac { 7 } { 2 } , 0 \right)$ 
D)  none

Question 9

Find the indicated intercept(s) of the graph of the function.2133:2139
-$y$-intercept of $f ( x ) = \frac { x ^ { 2 } - 10 x - 4 } { x ^ { 2 } + 13 x + 4 }$

Accepted Answer

A)  $( 0,13 )$ 
B)  $( 0 , - 1 )$ 
C)  $( 0 , - 4 )$ 
D)  none 
A)  $( 0,13 )$ 
B)  $( 0 , - 1 )$ 
C)  $( 0 , - 4 )$ 
D)  none

Question 10

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$$

Accepted Answer

A)  $f ( - 1 ) = 3$ and $f ( 0 ) = 7$; no 
B)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 6$; no 
C)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 6$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 6$; yes 
A)  $f ( - 1 ) = 3$ and $f ( 0 ) = 7$; no 
B)  $f ( - 1 ) = - 3$ and $f ( 0 ) = - 6$; no 
C)  $f ( - 1 ) = 3$ and $f ( 0 ) = - 6$; yes 
D)  $f ( - 1 ) = - 3$ and $f ( 0 ) = 6$; yes

Question 11

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)  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)  No

Question 12

Give the equation of the oblique asymptote, if any, of the function.
-$$h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 4 } { 5 x ^ { 2 } - 2 x + 5 }$$

Accepted Answer

A)  $y = \frac { 7 } { 5 } x$ 
B)  $y = x + \frac { 7 } { 5 }$ 
C)  $y = \frac { 7 } { 5 }$ 
D)  no oblique asymptote 
A)  $y = \frac { 7 } { 5 } x$ 
B)  $y = x + \frac { 7 } { 5 }$ 
C)  $y = \frac { 7 } { 5 }$ 
D)  no oblique asymptote

Question 13

Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { x ( x - 1 ) } { x ^ { 3 } + 49 x }$$

Accepted Answer

A)  $x = 0 , x = - 49$ 
B)  $y = 1$ 
C)  no horizontal asymptotes 
D)  $y = 0$ 
A)  $x = 0 , x = - 49$ 
B)  $y = 1$ 
C)  no horizontal asymptotes 
D)  $y = 0$

Question 14

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = \left( x + \frac { 1 } { 8 } \right) ^ { 2 } ( x - 2 ) ^ { 5 }$$

Accepted Answer

A)  above the $x$-axis: $\left( - \frac { 1 } { 8 } , 2 \right)$
below the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , ( 2 , \infty )$ 
B)  above the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right)$,
below the $x$-axis: $\left( - \frac { 1 } { 8 } , 2 \right)$ 
C)  above the $x$-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$
below the $x$-axis: $( 2 , \infty )$ 
D)  above the $x$-axis: $( 2 , \infty )$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$ 
A)  above the $x$-axis: $\left( - \frac { 1 } { 8 } , 2 \right)$
below the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , ( 2 , \infty )$ 
B)  above the x-axis: $\left( - \infty , - \frac { 1 } { 8 } \right)$,
below the $x$-axis: $\left( - \frac { 1 } { 8 } , 2 \right)$ 
C)  above the $x$-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$
below the $x$-axis: $( 2 , \infty )$ 
D)  above the $x$-axis: $( 2 , \infty )$
below the $x$-axis: $\left( - \infty , - \frac { 1 } { 8 } \right) , \left( - \frac { 1 } { 8 } , 2 \right)$

Question 15

Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { 16 x ^ { 5 } - 4 } { x - x ^ { 3 } }$$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$

Accepted Answer

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

Question 18

Find the indicated intercept(s) of the graph of the function.2133:2139
-$x$-intercepts of $f ( x ) = \frac { 2 x + 5 } { x - 5 }$

Accepted Answer

A)  $\left( \frac { 5 } { 2 } , 0 \right)$ 
B)  $( - 5,0 )$ 
C)  $\left( - \frac { 5 } { 2 } , 0 \right)$ 
D)  $( 5,0 )$ 
A)  $\left( \frac { 5 } { 2 } , 0 \right)$ 
B)  $( - 5,0 )$ 
C)  $\left( - \frac { 5 } { 2 } , 0 \right)$ 
D)  $( 5,0 )$

Question 19

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

Accepted Answer

A)  $( - 3,0 )$ 
B)  $( 3,0 )$ 
C)  $( 2,0 )$ 
D)  none 
A)  $( - 3,0 )$ 
B)  $( 3,0 )$ 
C)  $( 2,0 )$ 
D)  none

Question 20

Give the equation of the horizontal asymptote, if any, of the function.
-$$g ( x ) = \frac { x ^ { 2 } + 3 x - 3 } { x - 3 }$$

Accepted Answer

A)  $y = 3$ 
B)  $y = 1$ 
C)  $y = 0$ 
D)  no horizontal asymptotes 
A)  $y = 3$ 
B)  $y = 1$ 
C)  $y = 0$ 
D)  no horizontal asymptotes

Solve the inequality. - $\frac { x + 25 } { x + 4 } < 9$

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

Solve the inequality. - $\frac { 15 x } { 5 - x } \geq 5 x$

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

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 15 x + 6 } { 2 x }$

Find the domain of the rational function. - $f ( x ) = \frac { - 2 x ( x + 2 ) } { 5 x ^ { 2 } - 3 x - 8 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x$ -intercepts of $f ( x ) = \frac { ( x - 8 ) ( 2 x + 7 ) } { x ^ { 2 } + 3 x - 4 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 10 x - 4 } { x ^ { 2 } + 13 x + 4 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]$

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

Give the equation of the oblique asymptote, if any, of the function. - $h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 4 } { 5 x ^ { 2 } - 2 x + 5 }$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x ( x - 1 ) } { x ^ { 3 } + 49 x }$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = \left( x + \frac { 1 } { 8 } \right) ^ { 2 } ( x - 2 ) ^ { 5 }$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { 16 x ^ { 5 } - 4 } { x - x ^ { 3 } }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x$ -intercepts of $f ( x ) = \frac { 2 x + 5 } { x - 5 }$

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

Give the equation of the horizontal asymptote, if any, of the function. - $g ( x ) = \frac { x ^ { 2 } + 3 x - 3 } { x - 3 }$

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

Review

Filters

Exam 3: Polynomial and Rational Functions

Solve the inequality. - x+25x+4<9\frac { x + 25 } { x + 4 } < 9x+4x+25​<9

Use transformations of the graph o y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 to graph the function. - f(x)=12(x+4)4+3f ( x ) = \frac { 1 } { 2 } ( x + 4 ) ^ { 4 } + 3f(x)=21​(x+4)4+3 A) B) C) D)

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

Solve the inequality. - 15x5−x≥5x\frac { 15 x } { 5 - x } \geq 5 x5−x15x​≥5x

Find the x- and y-intercepts of f. - f(x)=x2(x−1)(x−5)f ( x ) = x ^ { 2 } ( x - 1 ) ( x - 5 )f(x)=x2(x−1)(x−5)

Find the indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=x2−15x+62xf ( x ) = \frac { x ^ { 2 } - 15 x + 6 } { 2 x }f(x)=2xx2−15x+6​

Find the domain of the rational function. - f(x)=−2x(x+2)5x2−3x−8f ( x ) = \frac { - 2 x ( x + 2 ) } { 5 x ^ { 2 } - 3 x - 8 }f(x)=5x2−3x−8−2x(x+2)​

Find the indicated intercept(s) of the graph of the function.2133:2139 - xxx -intercepts of f(x)=(x−8)(2x+7)x2+3x−4f ( x ) = \frac { ( x - 8 ) ( 2 x + 7 ) } { x ^ { 2 } + 3 x - 4 }f(x)=x2+3x−4(x−8)(2x+7)​

Find the indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=x2−10x−4x2+13x+4f ( x ) = \frac { x ^ { 2 } - 10 x - 4 } { x ^ { 2 } + 13 x + 4 }f(x)=x2+13x+4x2−10x−4​

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=−6x4−3x2+6;[−1,0]f ( x ) = - 6 x ^ { 4 } - 3 x ^ { 2 } + 6 ; [ - 1,0 ]f(x)=−6x4−3x2+6;[−1,0]

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)=6x3+16x2+18x−8;c=13f ( x ) = 6 x ^ { 3 } + 16 x ^ { 2 } + 18 x - 8 ; c = \frac { 1 } { 3 }f(x)=6x3+16x2+18x−8;c=31​

Give the equation of the oblique asymptote, if any, of the function. - h(x)=7x2−9x−45x2−2x+5h ( x ) = \frac { 7 x ^ { 2 } - 9 x - 4 } { 5 x ^ { 2 } - 2 x + 5 }h(x)=5x2−2x+57x2−9x−4​

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=x(x−1)x3+49xf ( x ) = \frac { x ( x - 1 ) } { x ^ { 3 } + 49 x }f(x)=x3+49xx(x−1)​

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - f(x)=(x+18)2(x−2)5f ( x ) = \left( x + \frac { 1 } { 8 } \right) ^ { 2 } ( x - 2 ) ^ { 5 }f(x)=(x+81​)2(x−2)5

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=16x5−4x−x3f ( x ) = \frac { 16 x ^ { 5 } - 4 } { x - x ^ { 3 } }f(x)=x−x316x5−4​

Graph the function. - f(x)=x2−4x(x−2)2f ( x ) = \frac { x ^ { 2 } - 4 x } { ( x - 2 ) ^ { 2 } }f(x)=(x−2)2x2−4x​ A) B) C) D)

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x3+7x2−16x+18;x+9f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9f(x)=x3+7x2−16x+18;x+9

Find the indicated intercept(s) of the graph of the function.2133:2139 - xxx -intercepts of f(x)=2x+5x−5f ( x ) = \frac { 2 x + 5 } { x - 5 }f(x)=x−52x+5​

Find the indicated intercept(s) of the graph of the function.2133:2139 - xxx -intercepts of f(x)=x−3x2+2x−3f ( x ) = \frac { x - 3 } { x ^ { 2 } + 2 x - 3 }f(x)=x2+2x−3x−3​

Give the equation of the horizontal asymptote, if any, of the function. - g(x)=x2+3x−3x−3g ( x ) = \frac { x ^ { 2 } + 3 x - 3 } { x - 3 }g(x)=x−3x2+3x−3​