Question 1

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

Accepted Answer

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

Question 2

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 3

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$$

Accepted Answer

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

Question 4

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)  $\mathrm { y } = 3$ 
B)  $\mathrm { y } = 1$ 
C)  $y = 0$ 
D)  no horizontal asymptotes 
A)  $\mathrm { y } = 3$ 
B)  $\mathrm { y } = 1$ 
C)  $y = 0$ 
D)  no horizontal asymptotes

Question 5

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.
-$$f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10$$

Accepted Answer

A)  $- 5 , - 1 , \frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) ( x + 1 ) ( x + 5 )$ 
B)  $\frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) \left( x ^ { 2 } + 5 \right)$ 
C)  $10 ; f ( x ) = ( x - 10 ) \left( 5 x ^ { 2 } + 1 \right)$ 
D)  $5 , \frac { 2 } { 5 } , 1 ; f ( x ) = ( 5 x - 2 ) ( x - 1 ) ( x - 5 )$ 
A)  $- 5 , - 1 , \frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) ( x + 1 ) ( x + 5 )$ 
B)  $\frac { 2 } { 5 } ; f ( x ) = ( 5 x - 2 ) \left( x ^ { 2 } + 5 \right)$ 
C)  $10 ; f ( x ) = ( x - 10 ) \left( 5 x ^ { 2 } + 1 \right)$ 
D)  $5 , \frac { 2 } { 5 } , 1 ; f ( x ) = ( 5 x - 2 ) ( x - 1 ) ( x - 5 )$

Question 6

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

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 7

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

Accepted Answer

A)  Yes; degree 1 
B)  No; it is a product 
C)  No; $x$ is raised to non-integer power 
D)  Yes; degree 2 
A)  Yes; degree 1 
B)  No; it is a product 
C)  No; $x$ is raised to non-integer power 
D)  Yes; degree 2

Question 8

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 9

Solve the problem.
-For what positive numbers will the cube of a number exceed 9 times its square?

Accepted Answer

A)  $\{ x \mid x > 9 \}$ 
B)  $x \mid 0  81 \}$ 
A)  $\{ x \mid x > 9 \}$ 
B)  $x \mid 0  81 \}$

Question 10

Use the given zero to find the remaining zeros of the function.
-$f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196$; zero: $- 2 i$

Accepted Answer

A)  $2 i , 7 i , - 7 i$ 
B)  $2 \mathrm { i } , 7 , - 7$ 
C)  $2 \mathrm { i } , 14 \mathrm { i } , - 14 \mathrm { i }$ 
D)  $2 \mathrm { i } , 14 , - 14$ 
A)  $2 i , 7 i , - 7 i$ 
B)  $2 \mathrm { i } , 7 , - 7$ 
C)  $2 \mathrm { i } , 14 \mathrm { i } , - 14 \mathrm { i }$ 
D)  $2 \mathrm { i } , 14 , - 14$

Question 11

Graph the function.
-$$f ( x ) = \frac { x } { x ^ { 2 } - 9 }$$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 12

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 13

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
-Degree 5; zeros: $- 2 , \mathrm { i } , - 2 \mathrm { i }$

Accepted Answer

A)  $2 , - \mathrm { i } , 2 \mathrm { i }$ 
B)  $2,2 \mathrm { i }$ 
C)  $2 , - \mathrm { i }$ 
D)  $- \mathrm { i } , 2 \mathrm { i }$ 
A)  $2 , - \mathrm { i } , 2 \mathrm { i }$ 
B)  $2,2 \mathrm { i }$ 
C)  $2 , - \mathrm { i }$ 
D)  $- \mathrm { i } , 2 \mathrm { i }$

Question 14

Find the domain of the rational function.
-$$f ( x ) = \frac { 5 x } { ( x - 6 ) ( x + 8 ) }$$

Accepted Answer

A)  $\{ x \mid x \neq - 6 , x \neq 8 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq 6 , x \neq - 8 \}$ 
D)  $\{ x \mid x \neq 6 , x \neq - 8 , x \neq - 5 \}$ 
A)  $\{ x \mid x \neq - 6 , x \neq 8 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq 6 , x \neq - 8 \}$ 
D)  $\{ x \mid x \neq 6 , x \neq - 8 , x \neq - 5 \}$

Question 15

Solve the problem.
-A ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s = 128t - 16t2. For what intervals of time is the ball less than 112 above the
Ground (after it is tossed until it returns to the ground)?

Accepted Answer

A) $\{ x \mid 0 \sec x > 8 \mathrm { sec } \}$ B) $\{ x \mid 0 \sec x > 8 \mathrm { sec } \}$ C) $\{ x \mid 0 \mathrm { sec } x > 8 \mathrm { sec } \}$ D) $\{ x \mid 1 \sec < x < 7 \mathrm { sec } \}$ A) $\{ x \mid 0 \sec x > 8 \mathrm { sec } \}$ B) $\{ x \mid 0 \sec x > 8 \mathrm { sec } \}$ C) $\{ x \mid 0 \mathrm { sec } x > 8 \mathrm { sec } \}$ D) $\{ x \mid 1 \sec < x < 7 \mathrm { sec } \}$

Question 16

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

Accepted Answer

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

Question 17

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 18

Solve the inequality.
-$$x ( x + 5 ) \geq - 6$$

Accepted Answer

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

Question 19

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 20

Graph the function.
-$$f ( x ) = \frac { x ^ { 4 } - 1 } { x ^ { 2 } - 16 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

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

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

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

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. - $f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10$

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

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

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

Solve the problem. -For what positive numbers will the cube of a number exceed 9 times its square?

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196$ ; zero: $- 2 i$

Graph the function. - $f ( x ) = \frac { x } { x ^ { 2 } - 9 }$ $Graph the function. - f ( x ) = \frac { x } { x ^ { 2 } - 9 }$

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

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 5; zeros: $- 2 , \mathrm { i } , - 2 \mathrm { i }$

Find the domain of the rational function. - $f ( x ) = \frac { 5 x } { ( x - 6 ) ( x + 8 ) }$

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

Solve the inequality. - $x ( x + 5 ) \geq - 6$

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

Graph the function. - $f ( x ) = \frac { x ^ { 4 } - 1 } { x ^ { 2 } - 16 }$ $Graph the function. - f ( x ) = \frac { x ^ { 4 } - 1 } { x ^ { 2 } - 16 }$

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

Use the Factor Theorem to determine whether x - c is a factor of f(x). - 7x4+20x3−3x2+x−3;x+37 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 37x4+20x3−3x2+x−3;x+3

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​

Choose the one alternative that best completes the statement or answers the question. 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+3x−3x−3g ( x ) = \frac { x ^ { 2 } + 3 x - 3 } { x - 3 }g(x)=x−3x2+3x−3​

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)=5x3−2x2+25x−10f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } + 25 x - 10f(x)=5x3−2x2+25x−10

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 5; zeros: 2, −3i- 3 \mathrm { i }−3i , and 4−i4 - \mathrm { i }4−i

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)=x(x−5)f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )f(x)=x​(x​−5)

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