Question 1

Find the x- and y-intercepts of f.
-$f ( x ) = ( x + 10 ) ^ { 2 }$

Accepted Answer

A)  x-intercept: 10; y-intercept: 0 
B)  x-intercept: -10; y-intercept: 100 
C)  x-intercept: 10; y-intercept: 100 
D)  x-intercept: -10; y-intercept: 0 
A)  x-intercept: 10; y-intercept: 0 
B)  x-intercept: -10; y-intercept: 100 
C)  x-intercept: 10; y-intercept: 100 
D)  x-intercept: -10; y-intercept: 0

Question 2

Find the vertical asymptotes of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 3 } - 343 }$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = - 7 , x = 7$ 
C)  $x = 7$ 
D)  $x = 49$ 
A)  $x = - 7$ 
B)  $x = - 7 , x = 7$ 
C)  $x = 7$ 
D)  $x = 49$

Question 3

Solve the problem.
-The polynomial function $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$ has exactly one positive zero.
Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places.

Accepted Answer

A)  $0.10$ 
B)  $0.66$ 
C)  $0.33$ 
D)  $0.50$ 
A)  $0.10$ 
B)  $0.66$ 
C)  $0.33$ 
D)  $0.50$

Question 4

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]$$

Accepted Answer

A)  $f ( 1 ) = - 5$ and $f ( 2 ) = 13$; yes 
B)  $f ( 1 ) = 5$ and $f ( 2 ) = - 13$; yes 
C)  $f ( 1 ) = 5$ and $f ( 2 ) = 13$; no 
D)  $f ( 1 ) = - 5$ and $f ( 2 ) = - 13$; no 
A)  $f ( 1 ) = - 5$ and $f ( 2 ) = 13$; yes 
B)  $f ( 1 ) = 5$ and $f ( 2 ) = - 13$; yes 
C)  $f ( 1 ) = 5$ and $f ( 2 ) = 13$; no 
D)  $f ( 1 ) = - 5$ and $f ( 2 ) = - 13$; no

Question 5

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

Accepted Answer

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

Question 6

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
-Degree 4 ; zeros: $\mathrm { i } , 1 + \mathrm { i }$

Accepted Answer

A)  $- i , - 1 + i$ 
B)  $1 - \mathrm { i }$ 
C)  $- \mathrm { i } , 1 - \mathrm { i }$ 
D)  $- 1 + i , 1 - i$ 
A)  $- i , - 1 + i$ 
B)  $1 - \mathrm { i }$ 
C)  $- \mathrm { i } , 1 - \mathrm { i }$ 
D)  $- 1 + i , 1 - i$

Question 7

Give the equation of the horizontal asymptote, if any, of the function.
-$$h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$$

Accepted Answer

A)  $y = 4$ 
B)  no horizontal asymptote 
C)  $y = 0$ 
D)  $y = \frac { 1 } { 2 }$ 
A)  $y = 4$ 
B)  no horizontal asymptote 
C)  $y = 0$ 
D)  $y = \frac { 1 } { 2 }$

Question 8

Solve the inequality.
-$$x + \frac { 30 } { x } < 13$$

Accepted Answer

A)  $( - \infty , 0 )$ or $( 10 , \infty )$ 
B)  $( - \infty , 0 )$ or $( 3,10 )$ 
C)  $( 0,3 )$ or $( 3,10 )$ 
D)  $( 0,3 )$ or $( 10 , \infty )$ 
A)  $( - \infty , 0 )$ or $( 10 , \infty )$ 
B)  $( - \infty , 0 )$ or $( 3,10 )$ 
C)  $( 0,3 )$ or $( 3,10 )$ 
D)  $( 0,3 )$ or $( 10 , \infty )$

Question 9

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

Accepted Answer

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

Question 10

Find the domain of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$$

Accepted Answer

A)  all real numbers 
B)  $\{ x \mid x \neq - 3 , x \neq 5 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
D)  $\{ x \mid x \neq 3 , x \neq - 5 \}$ 
A)  all real numbers 
B)  $\{ x \mid x \neq - 3 , x \neq 5 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
D)  $\{ x \mid x \neq 3 , x \neq - 5 \}$

Question 11

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 12

Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 5; zeros: 2 , -3i, and 4 - i

Accepted Answer

A)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } + 72 x + 306$ 
B)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x - 306$ 
C)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x + 306$ 
D)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } - 72 x - 306$ 
A)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } + 72 x + 306$ 
B)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x - 306$ 
C)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 42 x ^ { 3 } - 124 x ^ { 2 } + 297 x + 306$ 
D)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } + 26 x ^ { 3 } - 124 x ^ { 2 } - 72 x - 306$

Question 13

Solve the equation in the real number system.
-$2 x ^ { 4 } - 15 x ^ { 3 } + 60 x ^ { 2 } - 115 x + 78 = 0$

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
-Degree 3 ; zeros: $- 3,3 - 5 i$

Accepted Answer

A)  $3 , - 3 + 5 i$ 
B)  $3 + 5 i$ 
C)  $3,3 + 5 i$ 
D)  $- 3 + 5 i$ 
A)  $3 , - 3 + 5 i$ 
B)  $3 + 5 i$ 
C)  $3,3 + 5 i$ 
D)  $- 3 + 5 i$

Question 16

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { 6 x ^ { 3 } + 22 x ^ { 2 } + 35 x + 31 } { 3 x + 5 }$$

Accepted Answer

A)  $y = 0$ 
B)  $y = 2 x + 5$ 
C)  no oblique asymptote 
D)  $y = 2 x ^ { 2 } + 4 x + 5$ 
A)  $y = 0$ 
B)  $y = 2 x + 5$ 
C)  no oblique asymptote 
D)  $y = 2 x ^ { 2 } + 4 x + 5$

Question 17

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

Accepted Answer

A)  $x = \frac { 8 } { 3 } , x = - 1$ 
B)  $x = - \frac { 8 } { 3 } , x = 1$ 
C)  $x = - \frac { 3 } { 8 } , x = 1$ 
D)  $x = \frac { 3 } { 8 } , x = - 1$ 
A)  $x = \frac { 8 } { 3 } , x = - 1$ 
B)  $x = - \frac { 8 } { 3 } , x = 1$ 
C)  $x = - \frac { 3 } { 8 } , x = 1$ 
D)  $x = \frac { 3 } { 8 } , x = - 1$

Question 18

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 3 } }$

Accepted Answer

A)  Yes; degree -3 
B)  Yes; degree 3 
C)  No; it is a ratio of polynomials 
D)  Yes; degree 4 
A)  Yes; degree -3 
B)  Yes; degree 3 
C)  No; it is a ratio of polynomials 
D)  Yes; degree 4

Question 19

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

Accepted Answer

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

Question 20

Solve the problem.
-$x ^ { 4 } < 81 x ^ { 2 }$

Accepted Answer

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

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 10 ) ^ { 2 }$

Find the vertical asymptotes of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 343 }$

Solve the problem. -The polynomial function $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$ has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places.

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: $\mathrm { i } , 1 + \mathrm { i }$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$

Solve the inequality. - $x + \frac { 30 } { x } < 13$

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

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

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 5; zeros: 2 , -3i, and 4 - i

Solve the equation in the real number system. - $2 x ^ { 4 } - 15 x ^ { 3 } + 60 x ^ { 2 } - 115 x + 78 = 0$

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

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: $- 3,3 - 5 i$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { 6 x ^ { 3 } + 22 x ^ { 2 } + 35 x + 31 } { 3 x + 5 }$

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

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 3 } }$

Solve the problem. - $x ^ { 4 } < 81 x ^ { 2 }$

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

Review

Filters

Exam 3: Polynomial and Rational Functions

Find the x- and y-intercepts of f. - f(x)=(x+10)2f ( x ) = ( x + 10 ) ^ { 2 }f(x)=(x+10)2

Find the vertical asymptotes of the rational function. - g(x)=xx3−343g ( x ) = \frac { x } { x ^ { 3 } - 343 }g(x)=x3−343x​

Solve the problem. -The polynomial function f(x)=6x3+19x2+8x−5f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5f(x)=6x3+19x2+8x−5 has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places.

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=5x3−7x2+4x−7;[1,2]f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]f(x)=5x3−7x2+4x−7;[1,2]

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)=x4−5f(x)=x^{4}-5f(x)=x4−5 A) B) C) D)

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: i,1+i\mathrm { i } , 1 + \mathrm { i }i,1+i

Give the equation of the horizontal asymptote, if any, of the function. - h(x)=4x3−5x−98x+3h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }h(x)=8x+34x3−5x−9​

Solve the inequality. - x+30x<13x + \frac { 30 } { x } < 13x+x30​<13

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)=−5x5f(x)=-5 x^{5}f(x)=−5x5 A) B) C) D)

Find the domain of the rational function. - f(x)=2x2−43x2+6x−45f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }f(x)=3x2+6x−452x2−4​

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​

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 5; zeros: 2 , -3i, and 4 - i

Solve the equation in the real number system. - 2x4−15x3+60x2−115x+78=02 x ^ { 4 } - 15 x ^ { 3 } + 60 x ^ { 2 } - 115 x + 78 = 02x4−15x3+60x2−115x+78=0

Find the indicated intercept(s) of the graph of the function.2133:2139 - x-intercepts of f(x)=x+1xx \text {-intercepts of } f ( x ) = x + \frac { 1 } { x }x-intercepts of f(x)=x+x1​

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: −3,3−5i- 3,3 - 5 i−3,3−5i

Give the equation of the oblique asymptote, if any, of the function. - f(x)=6x3+22x2+35x+313x+5f ( x ) = \frac { 6 x ^ { 3 } + 22 x ^ { 2 } + 35 x + 31 } { 3 x + 5 }f(x)=3x+56x3+22x2+35x+31​

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

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)=x4−7x3f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 3 } }f(x)=x3x4−7​

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)=3−(x−4)4f ( x ) = 3 - ( x - 4 ) ^ { 4 }f(x)=3−(x−4)4 A) B) C) D)

Solve the problem. - x4<81x2x ^ { 4 } < 81 x ^ { 2 }x4<81x2

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

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 10 ) ^ { 2 }$

Find the vertical asymptotes of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 343 }$

Solve the problem. -The polynomial function $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$ has exactly one positive zero. Use the Intermediate Value Theorem to approximate the zero correct to 2 decimal places.

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: $\mathrm { i } , 1 + \mathrm { i }$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$

Solve the inequality. - $x + \frac { 30 } { x } < 13$

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

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

Solve the equation in the real number system. - $2 x ^ { 4 } - 15 x ^ { 3 } + 60 x ^ { 2 } - 115 x + 78 = 0$

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

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: $- 3,3 - 5 i$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { 6 x ^ { 3 } + 22 x ^ { 2 } + 35 x + 31 } { 3 x + 5 }$

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

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 3 } }$

Solve the problem. - $x ^ { 4 } < 81 x ^ { 2 }$