Question 1

Solve the equation in the real number system.
-$$x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0$$

Accepted Answer

A)  $\{ 2,4 \}$ 
B)  $\{ - 4 , - 2,1 \}$ 
C)  $\{ - 4 , - 2 \}$ 
D)  $\{ - 1,2,4 \}$ 
A)  $\{ 2,4 \}$ 
B)  $\{ - 4 , - 2,1 \}$ 
C)  $\{ - 4 , - 2 \}$ 
D)  $\{ - 1,2,4 \}$

Question 2

Find the power function that the graph of f resembles for large values of |x|.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$$

Accepted Answer

A)  $y = x ^ { 3 }$ 
B)  $y = x ^ { 2 }$ 
C)  $y = - x ^ { 7 }$ 
D)  $y = x ^ { 7 }$ 
A)  $y = x ^ { 3 }$ 
B)  $y = x ^ { 2 }$ 
C)  $y = - x ^ { 7 }$ 
D)  $y = x ^ { 7 }$

Question 3

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }$.

Accepted Answer

A)  $( 5,0 ) , ( - 6,0 )$ 
B)  $( 6,0 ) , ( - 5,0 )$ 
C)  $( 5,0 ) , ( 0,0 )$ 
D)  $( - 30,0 )$ 
A)  $( 5,0 ) , ( - 6,0 )$ 
B)  $( 6,0 ) , ( - 5,0 )$ 
C)  $( 5,0 ) , ( 0,0 )$ 
D)  $( - 30,0 )$

Question 4

Find the vertical asymptotes of the rational function.
-$$f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$$

Accepted Answer

A)  $x = 16 , x = - 2$ 
B)  $x = 0 , x = 16$ 
C)  $x = - 4 , x = 4$ 
D)  $x = - 4 , x = 4 , x = - 2$ 
A)  $x = 16 , x = - 2$ 
B)  $x = 0 , x = 16$ 
C)  $x = - 4 , x = 4$ 
D)  $x = - 4 , x = 4 , x = - 2$

Question 5

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
-Degree 6; zeros: $- 7,3,7 - 5 i , - 3 + i$

Accepted Answer

A)  $7,7 + 5 i$ 
B)  $7,7 + 5 i , - 3 - i$ 
C)  $7 + 5 i , - 3 - i$ 
D)  $- 7 + 5 i , 3 - i$ 
A)  $7,7 + 5 i$ 
B)  $7,7 + 5 i , - 3 - i$ 
C)  $7 + 5 i , - 3 - i$ 
D)  $- 7 + 5 i , 3 - i$

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) = 5

Accepted Answer

A)  No; it is a constant 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; it contains no variables 
A)  No; it is a constant 
B)  Yes; degree 0 
C)  Yes; degree 1 
D)  No; it contains no variables

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.
-$$f ( x ) = x ^ { 3 / 2 } - x ^ { 6 } + 7$$

Accepted Answer

A)  Yes; degree $3 / 2$ 
B)  Yes; degree 3 
C)  Yes; degree 6 
D)  No; $x$ is raised to non-integer $3 / 2$ power 
A)  Yes; degree $3 / 2$ 
B)  Yes; degree 3 
C)  Yes; degree 6 
D)  No; $x$ is raised to non-integer $3 / 2$ power

Question 8

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

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 10 x + 20$ 
B)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 20$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 2 x + 20$ 
D)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 10 x + 20$ 
A)  $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } - 10 x + 20$ 
B)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 2 x + 20$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 2 x + 20$ 
D)  $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 10 x + 20$

Question 9

Solve the problem.
-Decide which of the rational functions might have the given graph.

Accepted Answer

A)  $R ( x ) = \frac { x - 2 } { ( x + 2 ) ^ { 2 } ( x - 3 ) ^ { 2 } }$ 
B)  $R ( x ) = \frac { 2 - x } { ( x + 2 ) ( x - 3 ) }$ 
C)  $R ( x ) = \frac { x + 2 } { ( x - 2 ) ( x + 3 ) }$ 
D)  $R ( x ) = \frac { x - 2 } { ( x + 2 ) ( x - 3 ) }$ 
A)  $R ( x ) = \frac { x - 2 } { ( x + 2 ) ^ { 2 } ( x - 3 ) ^ { 2 } }$ 
B)  $R ( x ) = \frac { 2 - x } { ( x + 2 ) ( x - 3 ) }$ 
C)  $R ( x ) = \frac { x + 2 } { ( x - 2 ) ( x + 3 ) }$ 
D)  $R ( x ) = \frac { x - 2 } { ( x + 2 ) ( x - 3 ) }$

Question 10

Write the word or phrase that best completes each statement or answers the question.
Analyze the graph of the given function f as follows:
(a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(b) Find the x- and y-intercepts of the graph.
(c) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(d) Graph f using a graphing utility.
(e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places.
(f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points.
(g) Find the domain of f. Use the graph to find the range of f.
(h) Use the graph to determine where f is increasing and where f is decreasing.
-$$f ( x ) = ( x + 3 ) ( x - 2 ) ^ { 2 }$$

Accepted Answer

(a) For large values of @#LAT-DLM&, the graph of @#LAT-DLM&

Question 11

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 12

Find the domain of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 3 } - 216 }$$

Accepted Answer

A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x | x z - 6 \rangle$ 
C)  $\{ x | x z - 6,6 \rangle$ 
D)  $\{ x \mid x \neq 36 \}$ 
A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x | x z - 6 \rangle$ 
C)  $\{ x | x z - 6,6 \rangle$ 
D)  $\{ x \mid x \neq 36 \}$

Question 13

Solve the inequality.
-$$\frac { 5 x ^ { 2 } - 4 x - 9 } { x + 5 } \leq 0$$

Accepted Answer

A)  $( - \infty , - 1 ]$ or $\left( \frac { 9 } { 5 } , \infty \right)$ 
B)  $( - \infty , - 5 )$ or $\left[ - 1 , \frac { 9 } { 5 } \right]$ 
C)  $( - 5 , - 1 ]$ or $\left( \frac { 9 } { 5 } , \infty \right)$ 
D)  $( - \infty , - 5 ]$ or $\left[ - 1 , \frac { 9 } { 5 } \right]$ 
A)  $( - \infty , - 1 ]$ or $\left( \frac { 9 } { 5 } , \infty \right)$ 
B)  $( - \infty , - 5 )$ or $\left[ - 1 , \frac { 9 } { 5 } \right]$ 
C)  $( - 5 , - 1 ]$ or $\left( \frac { 9 } { 5 } , \infty \right)$ 
D)  $( - \infty , - 5 ]$ or $\left[ - 1 , \frac { 9 } { 5 } \right]$

Question 14

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$g ( x ) = \frac { x } { x ^ { 3 } - 216 }$$

Accepted Answer

A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x \mid x \neq 36 \}$ 
C)  $\{ x \mid x \neq - 6 \}$ 
D)  $\{ x \mid x \neq - 6,6 \}$ 
A)  $\{ x \mid x \neq 6 \}$ 
B)  $\{ x \mid x \neq 36 \}$ 
C)  $\{ x \mid x \neq - 6 \}$ 
D)  $\{ x \mid x \neq - 6,6 \}$

Question 15

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x - 2 ) ( x - 6 )$$

Accepted Answer

A)  $x$-intercepts: 2, 6; y-intercept: 12 
B)  $x$-intercepts: 2, 6; y-intercept: $- 8$ 
C)  $x$-intercepts: $- 2 , - 6 ; y$-intercept: $- 8$ 
D)  $x$-intercepts: $- 2 , - 6$; y-intercept: 12 
A)  $x$-intercepts: 2, 6; y-intercept: 12 
B)  $x$-intercepts: 2, 6; y-intercept: $- 8$ 
C)  $x$-intercepts: $- 2 , - 6 ; y$-intercept: $- 8$ 
D)  $x$-intercepts: $- 2 , - 6$; y-intercept: 12

Question 16

Choose the one alternative that best completes the statement or answers the question.
-Which of the following polynomial functions might have the graph shown in the illustration below?

Accepted Answer

A)  $f ( x ) = x ( x - 2 ) ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = x ( x - 2 ) ^ { 2 } ( x - 1 )$ 
C)  $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$ 
D)  $f ( x ) = x ^ { 2 } ( x - 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
A)  $f ( x ) = x ( x - 2 ) ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = x ( x - 2 ) ^ { 2 } ( x - 1 )$ 
C)  $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$ 
D)  $f ( x ) = x ^ { 2 } ( x - 2 ) ^ { 2 } ( x - 1 ) ^ { 2 }$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A lens can be used to create an image of an object on the opposite side of the lens, such as the image created on a
movie screen. Every lens has a measurement called its focal length, f. The distance s1 of the object to the lens is
related to the distance s2 of the lens to the image by the function $$s _ { 1 } = \frac { f _ { 2 } } { s _ { 2 } - f }$$ For a lens with f = 0.3 m, what are the asymptotes of this function?

Accepted Answer

vertical asymptote:

Question 18

Use the graph to determine the domain and range of the function.
-

Accepted Answer

A)  domain: all real numbers
 range: $\{ y \mid y \neq 0 \}$ 
B)  domain: $\{ x \mid x \neq 0 \}$
range: all real numbers 
C)  domain: all real numbers
range: all real numbers 
D)  domain: $\{ x \mid x \neq 0 \}$  
range: $\{ y \mid y \neq 0 \}$ 
A)  domain: all real numbers
 range: $\{ y \mid y \neq 0 \}$ 
B)  domain: $\{ x \mid x \neq 0 \}$
range: all real numbers 
C)  domain: all real numbers
range: all real numbers 
D)  domain: $\{ x \mid x \neq 0 \}$  
range: $\{ y \mid y \neq 0 \}$

Question 19

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

Accepted Answer

A)  $y = x - 6$ 
B)  $x = y + 4$ 
C)  $y = x + 11$ 
D)  no oblique asymptote 
A)  $y = x - 6$ 
B)  $x = y + 4$ 
C)  $y = x + 11$ 
D)  no oblique asymptote

Question 20

Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }$$

Accepted Answer

A)  $y = 1$ 
B)  $y = 0$ 
C)  $y = - 5 , y = 5$ 
D)  no horizontal asymptotes 
A)  $y = 1$ 
B)  $y = 0$ 
C)  $y = - 5 , y = 5$ 
D)  no horizontal asymptotes

Solve the equation in the real number system. - $x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0$

Find the power function that the graph of f resembles for large values of |x|. - $f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }$ .

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: $- 7,3,7 - 5 i , - 3 + i$

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) = 5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = x ^ { 3 / 2 } - x ^ { 6 } + 7$

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

Solve the problem. -Decide which of the rational functions might have the given graph.

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

Find the domain of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 216 }$

Solve the inequality. - $\frac { 5 x ^ { 2 } - 4 x - 9 } { x + 5 } \leq 0$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $g ( x ) = \frac { x } { x ^ { 3 } - 216 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 2 ) ( x - 6 )$

Choose the one alternative that best completes the statement or answers the question. -Which of the following polynomial functions might have the graph shown in the illustration below?

Use the graph to determine the domain and range of the function. -

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

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }$

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 equation in the real number system. - x3+5x2+2x−8=0x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0x3+5x2+2x−8=0

Find the power function that the graph of f resembles for large values of |x|. - f(x)=−x2(x+4)3(x2−1)f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+4)3(x2−1)

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=x2−x−30x2+5f ( x ) = \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } + 5 }f(x)=x2+5x2−x−30​ .

Find the vertical asymptotes of the rational function. - f(x)=x+2x2−16f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }f(x)=x2−16x+2​

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: −7,3,7−5i,−3+i- 7,3,7 - 5 i , - 3 + i−7,3,7−5i,−3+i