Question 1

Solve the inequality.
-$$x ^ { 3 } > 4 x ^ { 2 }$$

Accepted Answer

A)  $( - \infty , 0 )$ or $( 4 , \infty )$ 
B)  $( 4 , \infty )$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 4 )$ 
A)  $( - \infty , 0 )$ or $( 4 , \infty )$ 
B)  $( 4 , \infty )$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 4 )$

Question 2

Find the indicated intercept(s) of the graph of the function.
-$x$-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 3

Give the equation of the horizontal asymptote, if any, of the function.
-$$g ( x ) = \frac { x ^ { 2 } + 1 x - 7 } { x - 7 }$$

Accepted Answer

A)  $y = 0$ 
B)  $y = 7$ 
C)  $y = 1$ 
D)  no horizontal asymptote 
A)  $y = 0$ 
B)  $y = 7$ 
C)  $y = 1$ 
D)  no horizontal asymptote

Question 4

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = 5 x ^ { 5 } - 3 x ^ { 3 } + 8 x ^ { 2 } - 1 ; [ - 2 , - 1 ]$$

Accepted Answer

A)  $f ( - 2 ) = 105$ and $f ( - 1 ) = - 5$; yes 
B)  $f ( - 2 ) = 105$ and $f ( - 1 ) = 5$; no 
C)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = 5$; yes 
D)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = - 5$; no 
A)  $f ( - 2 ) = 105$ and $f ( - 1 ) = - 5$; yes 
B)  $f ( - 2 ) = 105$ and $f ( - 1 ) = 5$; no 
C)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = 5$; yes 
D)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = - 5$; no

Question 5

Solve the equation in the real number system.
-$$x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$$

Accepted Answer

A)  $\{ - 4,4 \}$ 
B)  $\{ - 4,1 \}$ 
C)  $\{ - 1,1 \}$ 
D)  $\{ - 1,4 \}$ 
A)  $\{ - 4,4 \}$ 
B)  $\{ - 4,1 \}$ 
C)  $\{ - 1,1 \}$ 
D)  $\{ - 1,4 \}$

Question 6

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = \frac { 2 - x ^ { 4 } } { 9 }$

Accepted Answer

A)  Yes; degree 1 
B)  No; x is a negative term 
C)  No; it is a ratio 
D)  Yes; degree 4 
A)  Yes; degree 1 
B)  No; x is a negative term 
C)  No; it is a ratio 
D)  Yes; degree 4

Question 7

Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 3; zeros: $- 3$ and $3 - 2 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 11 x + 39$ 
B)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 52$ 
C)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$ 
D)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 5 x + 39$ 
A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 11 x + 39$ 
B)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 52$ 
C)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$ 
D)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 5 x + 39$

Question 8

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 9

Use the given zero to find the remaining zeros of the function.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39 \text {; zero: } - 3$$

Accepted Answer

A)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
B)  $3 + 2 i , 3 - 2 i$ 
C)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
D)  $6 + 4 \mathrm { i } , 6 - 4 \mathrm { i }$ 
A)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
B)  $3 + 2 i , 3 - 2 i$ 
C)  $1 + 2 \mathrm { i } , 1 - 2 \mathrm { i }$ 
D)  $6 + 4 \mathrm { i } , 6 - 4 \mathrm { i }$

Question 10

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

Accepted Answer

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

Question 11

Find the x- and y-intercepts of f.
-$$f ( x ) = x ^ { 2 } ( x - 4 ) ( x - 1 )$$

Accepted Answer

A)  $x$-intercepts: $0 , - 4 , - 1 ;$ y-intercept: 0 
B)  $x$-intercepts: $0,4,1$; y-intercept: 4 
C)  x-intercepts: $0,4,1$; y-intercept: 0 
D)  $x$-intercepts: $0 , - 4 , - 1$; y-intercept: 4 
A)  $x$-intercepts: $0 , - 4 , - 1 ;$ y-intercept: 0 
B)  $x$-intercepts: $0,4,1$; y-intercept: 4 
C)  x-intercepts: $0,4,1$; y-intercept: 0 
D)  $x$-intercepts: $0 , - 4 , - 1$; y-intercept: 4

Question 12

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$$

Accepted Answer

A)  $f ( 1 ) = 2$ and $f ( 2 ) = - 111$; yes 
B)  $f ( 1 ) = 2$ and $f ( 2 ) = 111$; no 
C)  $f ( 1 ) = - 2$ and $f ( 2 ) = 111$; yes 
D)  $f ( 1 ) = - 2$ and $f ( 2 ) = - 111$; no 
A)  $f ( 1 ) = 2$ and $f ( 2 ) = - 111$; yes 
B)  $f ( 1 ) = 2$ and $f ( 2 ) = 111$; no 
C)  $f ( 1 ) = - 2$ and $f ( 2 ) = 111$; yes 
D)  $f ( 1 ) = - 2$ and $f ( 2 ) = - 111$; no

Question 13

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$$

Accepted Answer

A)  above the $x$-axis: $( - 4,2 )$
below the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$ 
B)  above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$ 
C)  above the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$
below the $x$-axis: no intervals 
D)  above the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$
below the $x$-axis: $( - 4,2 )$ 
A)  above the $x$-axis: $( - 4,2 )$
below the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$ 
B)  above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$ 
C)  above the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$
below the $x$-axis: no intervals 
D)  above the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$
below the $x$-axis: $( - 4,2 )$

Question 14

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.
-$x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 = 0 ; 2 < r \leq 3$

Accepted Answer

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

Question 15

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 16

Find the indicated intercept(s) of the graph of the function.
-$y$-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 17

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$f ( x ) = \frac { - 2 x ( x + 2 ) } { 2 x ^ { 2 } - 3 x - 5 }$$

Accepted Answer

A)  $\left\{ x \mid x \neq - \frac { 5 } { 2 } , 1 \right\}$ 
B)  $\left\{ x \mid x \neq \frac { 2 } { 5 } , - 1 \right\}$ 
C)  $\left\{ x \mid x \neq \frac { 5 } { 2 } , - 1 \right\}$ 
D)  $\left\{ x \mid x \neq - \frac { 2 } { 5 } , 1 \right\}$ 
A)  $\left\{ x \mid x \neq - \frac { 5 } { 2 } , 1 \right\}$ 
B)  $\left\{ x \mid x \neq \frac { 2 } { 5 } , - 1 \right\}$ 
C)  $\left\{ x \mid x \neq \frac { 5 } { 2 } , - 1 \right\}$ 
D)  $\left\{ x \mid x \neq - \frac { 2 } { 5 } , 1 \right\}$

Question 19

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { 2 x ^ { 3 } + 11 x ^ { 2 } + 5 x - 1 } { x ^ { 2 } + 6 x + 5 }$$

Accepted Answer

A)  $y = 0$ 
B)  $y = 2 x - 1$ 
C)  $y = 2 x$ 
D)  $y = 2 x + 1$ 
A)  $y = 0$ 
B)  $y = 2 x - 1$ 
C)  $y = 2 x$ 
D)  $y = 2 x + 1$

Question 20

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

Accepted Answer

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

Solve the inequality. - $x ^ { 3 } > 4 x ^ { 2 }$

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

Give the equation of the horizontal asymptote, if any, of the function. - $g ( x ) = \frac { x ^ { 2 } + 1 x - 7 } { x - 7 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 5 x ^ { 5 } - 3 x ^ { 3 } + 8 x ^ { 2 } - 1 ; [ - 2 , - 1 ]$

Solve the equation in the real number system. - $x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { 2 - x ^ { 4 } } { 9 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 3; zeros: $- 3$ and $3 - 2 \mathrm { i }$

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

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39 \text {; zero: } - 3$

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

Find the x- and y-intercepts of f. - $f ( x ) = x ^ { 2 } ( x - 4 ) ( x - 1 )$

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

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. - $x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 = 0 ; 2 < r \leq 3$

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

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

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $f ( x ) = \frac { - 2 x ( x + 2 ) } { 2 x ^ { 2 } - 3 x - 5 }$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { 2 x ^ { 3 } + 11 x ^ { 2 } + 5 x - 1 } { x ^ { 2 } + 6 x + 5 }$

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

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. - x3>4x2x ^ { 3 } > 4 x ^ { 2 }x3>4x2

Find the indicated intercept(s) of the graph of the function. - 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+1x−7x−7g ( x ) = \frac { x ^ { 2 } + 1 x - 7 } { x - 7 }g(x)=x−7x2+1x−7​

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=5x5−3x3+8x2−1;[−2,−1]f ( x ) = 5 x ^ { 5 } - 3 x ^ { 3 } + 8 x ^ { 2 } - 1 ; [ - 2 , - 1 ]f(x)=5x5−3x3+8x2−1;[−2,−1]

Solve the equation in the real number system. - x4−8x3+16x2+8x−17=0x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0x4−8x3+16x2+8x−17=0

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)=2−x49f ( x ) = \frac { 2 - x ^ { 4 } } { 9 }f(x)=92−x4​

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 3; zeros: −3- 3−3 and 3−2i3 - 2 \mathrm { i }3−2i

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​

Use the given zero to find the remaining zeros of the function. - f(x)=x3−3x2−5x+39; zero: −3f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39 \text {; zero: } - 3f(x)=x3−3x2−5x+39; zero: −3