Question 1

Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree: 4; zeros: $1 , - 1$, and $4 - 2 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x + 17$ 
B)  $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x - 17$ 
C)  $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x + 17$ 
D)  $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17$ 
A)  $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x + 17$ 
B)  $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 16 x ^ { 2 } - 8 x - 17$ 
C)  $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x + 17$ 
D)  $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17$

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

Accepted Answer

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

Question 3

Solve the problem.
-$$x ^ { 2 } + 7 x \geq 0$$

Accepted Answer

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

Question 4

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

Accepted Answer

A)  no oblique asymptote 
B)  y = x + 2 
C)  y = 3x + 2 
D)  y = 3 
A)  no oblique asymptote 
B)  y = x + 2 
C)  y = 3x + 2 
D)  y = 3

Question 5

Find all zeros of the function and write the polynomial as a product of linear factors.
-$$f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$$

Accepted Answer

A)  $f ( x ) = ( x + 1 ) ( x + 5 + i \sqrt { 2 } ) ( x - 1 - i \sqrt { 2 } )$ 
B)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x + 5 - i )$ 
C)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x - 5 - i )$ 
D)  $f ( x ) = ( x - 1 ) ( x + 5 + i \sqrt { 2 } ) ( x + 5 - i \sqrt { 2 } )$ 
A)  $f ( x ) = ( x + 1 ) ( x + 5 + i \sqrt { 2 } ) ( x - 1 - i \sqrt { 2 } )$ 
B)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x + 5 - i )$ 
C)  $f ( x ) = ( x + 1 ) ( x + 5 + i ) ( x - 5 - i )$ 
D)  $f ( x ) = ( x - 1 ) ( x + 5 + i \sqrt { 2 } ) ( x + 5 - i \sqrt { 2 } )$

Question 6

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1.
-Zeros: 0, - 7, 6; degree 3 A) $f ( x ) = x ^ { 3 } + x ^ { 2 } + x - 42$

Accepted Answer

B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$ 
C)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$ 
B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$ 
C)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$

Question 7

Find the domain of the rational function.
-$$R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 4 x - 12 }$$

Accepted Answer

A)  $\{ x \mid x \neq 6,2 \}$ 
B)  $\{ x \mid x \neq - 12,1 \}$ 
C)  $\{ x \mid x \neq 6 , - 2 \}$ 
D)  $\{ x \mid x \neq - 6,2 \}$ 
A)  $\{ x \mid x \neq 6,2 \}$ 
B)  $\{ x \mid x \neq - 12,1 \}$ 
C)  $\{ x \mid x \neq 6 , - 2 \}$ 
D)  $\{ x \mid x \neq - 6,2 \}$

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.   A) $f ( x ) = x + 2$

Accepted Answer

B)  $f ( x ) = x + \frac { 2 } { x }$ 
C)  $f ( x ) = x + \frac { 1 } { x }$ 
D)  $f ( x ) = 2 x + \frac { 1 } { x }$ 
B)  $f ( x ) = x + \frac { 2 } { x }$ 
C)  $f ( x ) = x + \frac { 1 } { x }$ 
D)  $f ( x ) = 2 x + \frac { 1 } { x }$

Question 10

Solve the problem.
-A closed box with a square base has to have a volume of 16,000 cubic inches. Find a function for the surface area of the box. A) $S ( x ) = x ^ { 2 } + \frac { 64,000 } { x }$

Accepted Answer

B)  $S ( x ) = 2 x ^ { 2 } + \frac { 64,000 } { x }$ 
C)  $S ( x ) = 2 x ^ { 2 } + \frac { 16,000 } { x }$ 
D)  $S ( x ) = 2 x ^ { 2 } + \frac { 96,000 } { x }$ 
B)  $S ( x ) = 2 x ^ { 2 } + \frac { 64,000 } { x }$ 
C)  $S ( x ) = 2 x ^ { 2 } + \frac { 16,000 } { x }$ 
D)  $S ( x ) = 2 x ^ { 2 } + \frac { 96,000 } { x }$

Question 11

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
-Degree 5; zeros: $8,2 + 5 i , - 8 i$

Accepted Answer

A)  $- 8,2 - 5 i , 8 i$ 
B)  $- 2 - 5 i , 8 i$ 
C)  $- 2 + 5 i , 8 i$ 
D)  $2 - 5 i , 8 i$ 
A)  $- 8,2 - 5 i , 8 i$ 
B)  $- 2 - 5 i , 8 i$ 
C)  $- 2 + 5 i , 8 i$ 
D)  $2 - 5 i , 8 i$

Question 12

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

Accepted Answer

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

Question 13

Use the given zero to find the remaining zeros of the function.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; \text { zero: } 1 + i$

Accepted Answer

A)  1 - i, 4 
B)  -4, 4 
C)  1 - i, 4i 
D)  1 - i, -4 
A)  1 - i, 4 
B)  -4, 4 
C)  1 - i, 4i 
D)  1 - i, -4

Question 14

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 5 ) ( x - 4 ) ( x + 4 )$$

Accepted Answer

A)  $x$-intercepts: $- 5 , - 4,4 ; y$-intercept: 80 
B)  x-intercepts: $- 5 , - 4,4$; y-intercept: $- 80$ 
C)  $x$-intercepts: $- 4,4,5 ; y$-intercept: 80 
D)  $x$-intercepts: $- 4,4,5 ; y$-intercept: $- 80$ 
A)  $x$-intercepts: $- 5 , - 4,4 ; y$-intercept: 80 
B)  x-intercepts: $- 5 , - 4,4$; y-intercept: $- 80$ 
C)  $x$-intercepts: $- 4,4,5 ; y$-intercept: 80 
D)  $x$-intercepts: $- 4,4,5 ; y$-intercept: $- 80$

Question 15

Use the graph to determine the domain and range of the function.
-  A) domain: $\{ x \mid x \leq 0$ or $x > 1 \}$
range: $\{ y \mid y \neq - 2 , y \neq 2 \}$

Accepted Answer

B)  domain: all real numbers  
range: all real numbers 
C)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$
range: $\{ y \mid y \leq 0$ or $y \geq 1 \}$ 
D)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$  
range: $\{ y \mid y \leq 0$ or $y > 1 \}$ 
B)  domain: all real numbers  
range: all real numbers 
C)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$
range: $\{ y \mid y \leq 0$ or $y \geq 1 \}$ 
D)  domain: $\{ x \mid x \neq - 2 , x \neq 2 \}$  
range: $\{ y \mid y \leq 0$ or $y > 1 \}$

Question 16

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

Accepted Answer

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

Question 17

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
-$$f ( x ) = 5 x ^ { 5 } - 3 x ^ { 3 } + 8 x ^ { 2 } - 1 ; [ - 2 , - 1 ]$$

Accepted Answer

A)  $f ( - 2 ) = 105$ and $f ( - 1 ) = - 5$; yes 
B)  $f ( - 2 ) = 105$ and $f ( - 1 ) = 5$; no 
C)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = 5$; yes 
D)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = - 5$; no 
A)  $f ( - 2 ) = 105$ and $f ( - 1 ) = - 5$; yes 
B)  $f ( - 2 ) = 105$ and $f ( - 1 ) = 5$; no 
C)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = 5$; yes 
D)  $f ( - 2 ) = - 105$ and $f ( - 1 ) = - 5$; no

Question 18

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

Accepted Answer

A)  $y = 0$ 
B)  $y = 9$ 
C)  $y = 4$ 
D)  no horizontal asymptotes 
A)  $y = 0$ 
B)  $y = 9$ 
C)  $y = 4$ 
D)  no horizontal asymptotes

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

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 $$\mathrm { s } = 128 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$$ . For what intervals of time is the ball less than 112 above the
Ground (after it is tossed until it returns to the ground)? A) $\{ x \mid 0 \mathrm { sec }  x > 8 \mathrm { sec } \}$

Accepted Answer

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

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: $1 , - 1$ , and $4 - 2 \mathrm { i }$

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

Solve the problem. - $x ^ { 2 } + 7 x \geq 0$

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

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 36 x + 26$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: 0, - 7, 6; degree 3 A) $f ( x ) = x ^ { 3 } + x ^ { 2 } + x - 42$ B) $f ( x ) = x ^ { 3 } + x ^ { 2 } + x + 42$ C) $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$ D) $f ( x ) = x ^ { 3 } + x ^ { 2 } + 42 x$

Find the domain of the rational function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 4 x - 12 }$

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

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 5; zeros: $8,2 + 5 i , - 8 i$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; \text { zero: } 1 + i$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 5 ) ( x - 4 ) ( x + 4 )$

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

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = 5 x ^ { 5 } - 3 x ^ { 3 } + 8 x ^ { 2 } - 1 ; [ - 2 , - 1 ]$

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

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

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

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Exam 3: Polynomial and Rational Functions

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: 1,−11 , - 11,−1 , and 4−2i4 - 2 \mathrm { i }4−2i

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)=−2x5+x3−x2+3f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3f(x)=−2x5+x3−x2+3

Solve the problem. - x2+7x≥0x ^ { 2 } + 7 x \geq 0x2+7x≥0