Question 1

Find the indicated intercept(s) of the graph of the function.2133:2139
-$y$-intercept of $f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }$

Accepted Answer

A)  $( 0,3 )$ 
B)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C)  $( 0,12 )$ 
D)  none 
A)  $( 0,3 )$ 
B)  $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C)  $( 0,12 )$ 
D)  none

Question 2

Solve the problem.
-For the polynomial function f(x) $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 11 x - 4$ a) Find the x- and y-intercepts of the graph of f. Round to two decimal places, if necessary.
b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
c) End behavior: find the power function that the graph of f resembles for large values of |x $| x |$ d) Use a graphing utility to graph the function.Approximate the local maxima rounded to two decimal places, if
necessary. Approximate the local minima rounded to two decimal places, if necessary.
e) Determine the number of turning points on the graph.
f) Put all the information together, and connect the points with a smooth, continuous curve to obtain the graph of f.

Accepted Answer

a) The @#LAT-DLM&-intercepts are @#LAT-DLM&, and 2.94. The @#LAT-DLM&-

Question 3

Use the given zero to find the remaining zeros of the function.
-$$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 i$$

Accepted Answer

A)  $- 3 - 2 i , 1$ 
B)  $- 3 - 2 i , - 1$ 
C)  $2 - 3 i , - 1$ 
D)  $2 - 3 \mathrm { i } , 1$ 
A)  $- 3 - 2 i , 1$ 
B)  $- 3 - 2 i , - 1$ 
C)  $2 - 3 i , - 1$ 
D)  $2 - 3 \mathrm { i } , 1$

Question 4

Solve the equation in the real number system.
-$$2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right\}$
В) $\left\{ - \frac { \sqrt { 10 } } { 2 } , \frac { \sqrt { 10 } } { 2 } \right\}$ 
C)  $\{ 1 , - 2 \}$ 
D)  $\{ - 1,2 \}$ 
A)  $\left\{ - \frac { 5 } { 2 } , \frac { 5 } { 2 } \right\}$
В) $\left\{ - \frac { \sqrt { 10 } } { 2 } , \frac { \sqrt { 10 } } { 2 } \right\}$ 
C)  $\{ 1 , - 2 \}$ 
D)  $\{ - 1,2 \}$

Question 5

Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$$

Accepted Answer

A)  $x = y + 4$ 
B)  $y = x - 12$ 
C)  $y = x + 4$ 
D)  no oblique asymptotes 
A)  $x = y + 4$ 
B)  $y = x - 12$ 
C)  $y = x + 4$ 
D)  no oblique asymptotes

Question 6

Graph the function.
-$$f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }$$
 
 A)

Accepted Answer

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

Question 7

Solve the problem.
-Decide which of the rational functions might have the given graph.   A) $R ( x ) = \frac { x - 2 } { ( x + 2 ) ^ { 2 } ( x - 3 ) ^ { 2 } }$

Accepted Answer

B)  $R ( x ) = \frac { 2 - x } { ( x + 2 ) ( x - 3 ) }$ 
C)  $R ( x ) = \frac { x + 2 } { ( x - 2 ) ( x + 3 ) }$ 
D)  $R ( x ) = \frac { x - 2 } { ( x + 2 ) ( x - 3 ) }$ 
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 8

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
-$f ( x ) = x ^ { 5 } - 2.9 x ^ { 4 } - 13.51 x ^ { 3 } + 28.816 x ^ { 2 } + 37.76 x - 5.567$

Accepted Answer

A)  5; 2 or 0 positive zeros; 2 or 0 negative zeros 
B)  5; 2 or 0 positive zeros; 3 or 1 negative zeros 
C)  5; 3 or 1 positive zeros; 3 or 1 negative zeros 
D)  5; 3 or 1 positive zeros; 2 or 0 negative zeros 
A)  5; 2 or 0 positive zeros; 2 or 0 negative zeros 
B)  5; 2 or 0 positive zeros; 3 or 1 negative zeros 
C)  5; 3 or 1 positive zeros; 3 or 1 negative zeros 
D)  5; 3 or 1 positive zeros; 2 or 0 negative zeros

Question 9

Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(39 - 0.2x) dollars. The cost of each calculator is $27. How many graphing calculators must be sold to make a profit (revenue - cost) of at least
$160.00? A) $\{ x \mid 21 < x < 19 \}$

Accepted Answer

B)  $\{ x \mid 5 < x < 25 \}$ 
C)  $\{ x \mid 20 < x < 40 \}$ 
D)  $\{ x \mid 22 < x < 38 \}$ 
B)  $\{ x \mid 5 < x < 25 \}$ 
C)  $\{ x \mid 20 < x < 40 \}$ 
D)  $\{ x \mid 22 < x < 38 \}$

Question 10

Solve the problem.
-The formula y $$y = \frac { f x } { x - f }$$ models the relationships needed to focus an image where y is the distance between the film and
projector lens, x is the distance between the move screen and the projector lens, and f is the focal length.
a) Sketch the graph of this rational function for f = 5 centimeters.   b) Bob and Carol are showing home movies. Use the graph to describe the desired distance between the film and the
projector lens as Carol moves the projector further from the screen.

Accepted Answer

a) @#IMG-DLM& b) To remain focused, the desired di

Question 11

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

Accepted Answer

A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq - 5 \}$ 
C)  $\{ x \mid x \neq 5 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq 0 \}$ 
B)  $\{ x \mid x \neq - 5 \}$ 
C)  $\{ x \mid x \neq 5 \}$ 
D)  all real numbers

Question 12

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.
-$$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$$

Accepted Answer

A)  $3 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 4 \right)$ 
B)  $- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $- 3 , - 2,3,2 ; f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 2 ) ( x + 2 )$ 
D)  $- 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 9 \right)$ 
A)  $3 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } + 4 \right)$ 
B)  $- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $- 3 , - 2,3,2 ; f ( x ) = ( x - 3 ) ( x + 3 ) ( x - 2 ) ( x + 2 )$ 
D)  $- 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) \left( x ^ { 2 } + 9 \right)$

Question 13

Find the indicated intercept(s) of the graph of the function.2133:2139
-$y$-intercept of $f ( x ) = \frac { x - 8 } { x ^ { 2 } + 15 x - 9 }$

Accepted Answer

A)  $\left( 0 , - \frac { 9 } { 8 } \right)$ 
B)  $\left( 0 , \frac { 8 } { 9 } \right)$ 
C)  $( 0,8 )$ 
D)  none 
A)  $\left( 0 , - \frac { 9 } { 8 } \right)$ 
B)  $\left( 0 , \frac { 8 } { 9 } \right)$ 
C)  $( 0,8 )$ 
D)  none

Question 14

Use the graph to determine the domain and range of the function.
-  A) domain: all real numbers
range: $\{ y \mid y \neq 0 \}$

Accepted Answer

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: $\{ y \mid y \neq 0 \}$ 
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 15

Find the indicated intercept(s) of the graph of the function.2133:2139
-$$x \text {-intercepts of } f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }$$

Accepted Answer

A)  (1, 0) 
B)  (5, 0) 
C)  (-1, 0), (1, 0) 
D)  (0, 0) 
A)  (1, 0) 
B)  (5, 0) 
C)  (-1, 0), (1, 0) 
D)  (0, 0)

Question 16

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: -1, 1, - 8; degree 3 A) $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + x + 8$

Accepted Answer

B)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + x - 8$ 
D)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$ 
B)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$ 
C)  $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + x - 8$ 
D)  $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Question 17

Find the indicated intercept(s) of the graph of the function.2133:2139
-$f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }$

Accepted Answer

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

Question 18

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.
-$f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$

Accepted Answer

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

Question 19

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 20

Find the x- and y-intercepts of f.
-$f ( x ) = - x ^ { 2 } ( x + 3 ) \left( x ^ { 2 } + 1 \right)$

Accepted Answer

A)  x-intercepts: -3, -1, 0, 1; y-intercept: 0 
B)  x-intercepts: -3, -1, 0; y-intercept: -3 
C)  x-intercepts: -3, 0; y-intercept: 0 
D)  x-intercepts: -3, -1, 0; y-intercept: 3 
A)  x-intercepts: -3, -1, 0, 1; y-intercept: 0 
B)  x-intercepts: -3, -1, 0; y-intercept: -3 
C)  x-intercepts: -3, 0; y-intercept: 0 
D)  x-intercepts: -3, -1, 0; y-intercept: 3

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 i$

Solve the equation in the real number system. - $2 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 0$

Give the equation of the oblique asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how many positive and how many negative zeros it may have. - $f ( x ) = x ^ { 5 } - 2.9 x ^ { 4 } - 13.51 x ^ { 3 } + 28.816 x ^ { 2 } + 37.76 x - 5.567$

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

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. - $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x - 8 } { x ^ { 2 } + 15 x - 9 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $x \text {-intercepts of } f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: -1, 1, - 8; degree 3 A) $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + x + 8$ B) $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$ C) $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + x - 8$ D) $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }$

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

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 3 ) \left( x ^ { 2 } + 1 \right)$

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 indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=x2−12x2+2x−4f ( x ) = \frac { x ^ { 2 } - 12 } { x ^ { 2 } + 2 x - 4 }f(x)=x2+2x−4x2−12​

Use the given zero to find the remaining zeros of the function. - f(x)=x3+7x2+19x+13; zero: −3+2if ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 19 x + 13 ; \text { zero: } - 3 + 2 if(x)=x3+7x2+19x+13; zero: −3+2i

Solve the equation in the real number system. - 2x4−2x3+x2−5x−10=02 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - 5 x - 10 = 02x4−2x3+x2−5x−10=0

Give the equation of the oblique asymptote, if any, of the function. - f(x)=x2+8x+5x+4f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }f(x)=x+4x2+8x+5​

Graph the function. - f(x)=x2−4x+4x2−3f ( x ) = \frac { x ^ { 2 } - 4 x + 4 } { x ^ { 2 } - 3 }f(x)=x2−3x2−4x+4​ A) B) C) D)

Find the domain of the rational function. - h(x)=8xx−5h ( x ) = \frac { 8 x } { x - 5 }h(x)=x−58x​

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)=x4−5x2−36f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36f(x)=x4−5x2−36

Find the indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=x−8x2+15x−9f ( x ) = \frac { x - 8 } { x ^ { 2 } + 15 x - 9 }f(x)=x2+15x−9x−8​

Find the indicated intercept(s) of the graph of the function.2133:2139 - x-intercepts of f(x)=5xx2−1x \text {-intercepts of } f ( x ) = \frac { 5 x } { x ^ { 2 } - 1 }x-intercepts of f(x)=x2−15x​

Find the indicated intercept(s) of the graph of the function.2133:2139 - f(x)=56x3+61x2−102x−110;x+118f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }f(x)=56x3+61x2−102x−110;x+811​

Solve the inequality. - 5x2−4x−9x+5≤0\frac { 5 x ^ { 2 } - 4 x - 9 } { x + 5 } \leq 0x+55x2−4x−9​≤0

Find the x- and y-intercepts of f. - f(x)=−x2(x+3)(x2+1)f ( x ) = - x ^ { 2 } ( x + 3 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+3)(x2+1)