Question 1

Solve the inequality.
-$$\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$$

Accepted Answer

A)  $( - \infty , - 3 ]$ or $( - 2 , - 1 )$ or $[ 1 , \infty )$ 
B)  $( - \infty , - 3 )$ or $( - 1 , \infty )$ 
C)  $( - \infty , 1 )$ or $( 3 , \infty )$ 
D)  $( - \infty , 1 ]$ or $[ 3 , \infty )$ 
A)  $( - \infty , - 3 ]$ or $( - 2 , - 1 )$ or $[ 1 , \infty )$ 
B)  $( - \infty , - 3 )$ or $( - 1 , \infty )$ 
C)  $( - \infty , 1 )$ or $( 3 , \infty )$ 
D)  $( - \infty , 1 ]$ or $[ 3 , \infty )$

Question 2

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 3

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.
-$$f ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + x + 4$$

Accepted Answer

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

Question 4

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

Question 5

Solve the inequality.
-$$\frac { 3 x } { 7 - x } < x$$

Accepted Answer

A)  $( 4,7 )$ 
B)  $( 7 , \infty )$ 
C)  $( 0,4 )$ or $( 7 , \infty )$ 
D)  $( - \infty , 4 )$ or $( 7 , \infty )$ 
A)  $( 4,7 )$ 
B)  $( 7 , \infty )$ 
C)  $( 0,4 )$ or $( 7 , \infty )$ 
D)  $( - \infty , 4 )$ or $( 7 , \infty )$

Question 6

Solve the problem.
-A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after t seconds is s = 160t - 16t2. For what interval of time is the ball more than 256 above the
Ground?

Accepted Answer

A)  $\{ x \mid 1.5 \mathrm { sec } < \mathrm { x } < 8.5 \mathrm { sec } \}$ 
B)  $\{ x \mid 2 \sec < x < 8 \mathrm { sec } \}$ 
C)  $\{ x \mid 4.5 \mathrm { sec } < x < 5.5 \mathrm { sec } \}$ 
D)  $\{ x \mid 7 \sec < x < 13 \mathrm { sec } \}$ 
A)  $\{ x \mid 1.5 \mathrm { sec } < \mathrm { x } < 8.5 \mathrm { sec } \}$ 
B)  $\{ x \mid 2 \sec < x < 8 \mathrm { sec } \}$ 
C)  $\{ x \mid 4.5 \mathrm { sec } < x < 5.5 \mathrm { sec } \}$ 
D)  $\{ x \mid 7 \sec < x < 13 \mathrm { sec } \}$

Question 7

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

Accepted Answer

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

Question 8

Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)$$

Accepted Answer

A)  $x$-intercepts: $- 5 , - 1,0,1$; y-intercept: 0 
B)  x-intercepts: $- 5,0,1 ;$ y-intercept: $- 5$ 
C)  $x$-intercepts: $- 1,0,1,5 ; y$-intercept: 0 
D)  $x$-intercepts: $- 5 , - 1,0,1$; $y$-intercept: $- 5$ 
A)  $x$-intercepts: $- 5 , - 1,0,1$; y-intercept: 0 
B)  x-intercepts: $- 5,0,1 ;$ y-intercept: $- 5$ 
C)  $x$-intercepts: $- 1,0,1,5 ; y$-intercept: 0 
D)  $x$-intercepts: $- 5 , - 1,0,1$; $y$-intercept: $- 5$

Question 9

Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$h ( x ) = \frac { x + 5 } { x ^ { 2 } - 36 }$$

Accepted Answer

A)  $\{ x \mid x \neq 0,36 \}$ 
B)  $\{ x \mid x \neq - 6,6 , - 5 \}$ 
C)  $\{ x \mid x \neq - 6,6 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq 0,36 \}$ 
B)  $\{ x \mid x \neq - 6,6 , - 5 \}$ 
C)  $\{ x \mid x \neq - 6,6 \}$ 
D)  all real numbers

Question 10

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 11

Solve the inequality.
-$$x ^ { 2 } - 5 x - 6 \leq 0$$

Accepted Answer

A)  $( - \infty , - 1 ]$ or $[ 6 , \infty )$ 
B)  $( - \infty , - 1 ]$ 
C)  $[ - 1,6 ]$ 
D)  $[ 6 , \infty )$ 
A)  $( - \infty , - 1 ]$ or $[ 6 , \infty )$ 
B)  $( - \infty , - 1 ]$ 
C)  $[ - 1,6 ]$ 
D)  $[ 6 , \infty )$

Question 12

Use the graph to find the oblique asymptote, if any, of the function.
-

Accepted Answer

A)  $y = - x$ 
B)  $y = x + 1$ 
C)  $y = x$ 
D)  no oblique asymptote 
A)  $y = - x$ 
B)  $y = x + 1$ 
C)  $y = x$ 
D)  no oblique asymptote

Question 13

Choose the one alternative that best completes the statement or answers the question.
-Economists use what is called a Leffer curve to predict the government revenue for tax rates from $0 \%$ to $100 \%$. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces $t$ maximum revenue. Suppose an economist produces this rational function
$R ( x ) = \frac { 10 x ( 100 - x ) } { 15 + x }$, where $R$ is revenue in millions at a tax rate of x percent. Use a graphing calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue?

Accepted Answer

A)  $31.4 \% ; \$ 464$ million 
B)  $29.7 \% ; \$ 467$ million 
C)  $28.1 \% ; \$ 470$ million 
D)  $26.5 \%$; $\$ 469$ million 
A)  $31.4 \% ; \$ 464$ million 
B)  $29.7 \% ; \$ 467$ million 
C)  $28.1 \% ; \$ 470$ million 
D)  $26.5 \%$; $\$ 469$ million

Question 14

Choose the one alternative that best completes the statement or answers the question.
-Economists use what is called a Leffer curve to predict the government revenue for tax rates from $0 \%$ to $100 \%$. Economists agree that the end points of the curve generate 0 revenue, but disagree on the tax rate that produces t maximum revenue. Suppose an economist produces this rational function
$R ( x ) = \frac { 10 x ( 100 - x ) } { 75 + x }$, where $R$ is revenue in millions at a tax rate of $x$ percent. Use a graphing calculator to graph the function. What tax rate produces the maximum revenue? What is the maximum revenue?

Accepted Answer

A)  $37.5 \% ; \$ 210$ million 
B)  $39.6 \% ; \$ 209$ million 
C)  $34.9 \% ; \$ 207$ million 
D)  $35.8 \% ; \$ 209$ million 
A)  $37.5 \% ; \$ 210$ million 
B)  $39.6 \% ; \$ 209$ million 
C)  $34.9 \% ; \$ 207$ million 
D)  $35.8 \% ; \$ 209$ million

Question 15

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the
form f(x) = (x - c)(quotient).
-$$f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 7 x ^ { 2 } + 61 x - 90 ; c = - 10$$

Accepted Answer

A)  Yes; $\mathrm { f } ( \mathrm { x } ) = ( \mathrm { x } + 10 ) \left( \mathrm { x } ^ { 3 } + 7 \mathrm { x } - 9 \right)$ 
B)  Yes; $f ( x ) = ( x - 10 ) \left( x ^ { 3 } + 7 x + 9 \right)$ 
C)  No 
D)  Yes; $f ( x ) = ( x + 10 ) \left( x ^ { 3 } + x - 9 \right)$ 
A)  Yes; $\mathrm { f } ( \mathrm { x } ) = ( \mathrm { x } + 10 ) \left( \mathrm { x } ^ { 3 } + 7 \mathrm { x } - 9 \right)$ 
B)  Yes; $f ( x ) = ( x - 10 ) \left( x ^ { 3 } + 7 x + 9 \right)$ 
C)  No 
D)  Yes; $f ( x ) = ( x + 10 ) \left( x ^ { 3 } + x - 9 \right)$

Question 16

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
-$$f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$$

Accepted Answer

A)  0 , multiplicity 1 
B)  $\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
C)  0 , multiplicity 1 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis 
A)  0 , multiplicity 1 
B)  $\sqrt { 5 }$, multiplicity 1 , touches $x$-axis; 
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
C)  0 , multiplicity 1 , crosses $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , touches $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , touches $x$-axis 
D)  0 , multiplicity 1 , touches $x$-axis;
$\sqrt { 5 }$, multiplicity 1 , crosses $x$-axis;
$- \sqrt { 5 }$, multiplicity 1 , crosses $x$-axis

Question 17

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

Accepted Answer

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

Question 18

Solve the inequality.
-$$\frac { 15 x } { 5 - x } \geq 5 x$$

Accepted Answer

A)  $[ 5 , \infty )$ 
B)  $( - \infty , 0 ]$ or $[ 2,5 )$ 
C)  $( - \infty , 2 ]$ or $[ 5 , \infty )$ 
D)  $[ 0,2 ]$ or $[ 5 , \infty )$ 
A)  $[ 5 , \infty )$ 
B)  $( - \infty , 0 ]$ or $[ 2,5 )$ 
C)  $( - \infty , 2 ]$ or $[ 5 , \infty )$ 
D)  $[ 0,2 ]$ or $[ 5 , \infty )$

Question 19

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: $- 1,1 , - 8$; degree 3

Accepted Answer

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

Question 20

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

Solve the inequality. - $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

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

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. - $f ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + x + 4$

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

Solve the inequality. - $\frac { 3 x } { 7 - x } < x$

Solve the problem. -A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after t seconds is s = 160t - 16t2. For what interval of time is the ball more than 256 above the Ground?

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

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)$

Choose the one alternative that best completes the statement or answers the question. Find the domain of the rational function. - $h ( x ) = \frac { x + 5 } { x ^ { 2 } - 36 }$

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

Solve the inequality. - $x ^ { 2 } - 5 x - 6 \leq 0$

Use the graph to find the oblique asymptote, if any, of the function. -

Use the Factor Theorem to determine whether x - c is a factor of f. If it is, write f in factored form, that is, write f in the form f(x) = (x - c)(quotient). - $f ( x ) = x ^ { 4 } + 10 x ^ { 3 } + 7 x ^ { 2 } + 61 x - 90 ; c = - 10$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \frac { 1 } { 5 } x \left( x ^ { 2 } - 5 \right)$

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

Solve the inequality. - $\frac { 15 x } { 5 - x } \geq 5 x$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 1,1 , - 8$ ; degree 3

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

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. - (x−1)(3−x)(x−2)2≤0\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0(x−2)2(x−1)(3−x)​≤0

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]

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)=4x3−2x2+x+4f ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + x + 4f(x)=4x3−2x2+x+4

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)

Solve the inequality. - 3x7−x<x\frac { 3 x } { 7 - x } < x7−x3x​<x