Question 1

Solve the equation in the real number system.
-$$x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$$

Accepted Answer

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

Question 2

Form a polynomial f(x) with real coefficients having the given degree and zeros.
-Degree 3: zeros: $1 + i$ and $- 9$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 16 x + 18$ 
B)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 18 x - 16$ 
C)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 16 x - 12$ 
A)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 16 x + 18$ 
B)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 18 x - 16$ 
C)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$ 
D)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } - 16 x - 12$

Question 3

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

Accepted Answer

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

Question 4

Give the equation of the horizontal asymptote, if any, of the function.
-$$R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 22 }$$

Accepted Answer

A)  $y = - 11 , y = 2$ 
B)  $y = - 3$ 
C)  no horizontal asymptotes 
D)  $y = 0$ 
A)  $y = - 11 , y = 2$ 
B)  $y = - 3$ 
C)  no horizontal asymptotes 
D)  $y = 0$

Question 5

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = 5 x + 7 x ^ { 3 }$

Accepted Answer

A)  Yes; degree 7 
B)  Yes; degree 1 
C)  Yes; degree 3 
D)  Yes; degree 5 
A)  Yes; degree 7 
B)  Yes; degree 1 
C)  Yes; degree 3 
D)  Yes; degree 5

Question 6

Use the graph to find the oblique asymptote, if any, of the function.
-A) y = -x

Accepted Answer

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

Question 7

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

Accepted Answer

A)  y = -4, y = 4 
B)  x = -4, x = 4, y = 1 
C)  y = 1 
D)  y = 0, y = 1 
A)  y = -4, y = 4 
B)  x = -4, x = 4, y = 1 
C)  y = 1 
D)  y = 0, y = 1

Question 8

Find the domain of the rational function.
-$$f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }$$

Accepted Answer

A)  $\left\{ x \mid x \neq - \frac { 1 } { 16 } , - \frac { 5 } { 16 } \right\}$ 
B)  $\left\{ x \mid x \neq - \frac { 1 } { 4 } , - \frac { 5 } { 4 } \right\}$ 
C)  $\left\{ x \mid x \neq \frac { 1 } { 4 } , \frac { 5 } { 4 } \right\}$ 
D)  $\left\{ x \mid x \neq - \frac { 5 } { 8 } , \frac { 5 } { 8 } \right\}$ 
A)  $\left\{ x \mid x \neq - \frac { 1 } { 16 } , - \frac { 5 } { 16 } \right\}$ 
B)  $\left\{ x \mid x \neq - \frac { 1 } { 4 } , - \frac { 5 } { 4 } \right\}$ 
C)  $\left\{ x \mid x \neq \frac { 1 } { 4 } , \frac { 5 } { 4 } \right\}$ 
D)  $\left\{ x \mid x \neq - \frac { 5 } { 8 } , \frac { 5 } { 8 } \right\}$

Question 9

Graph the function using transformations.
-$$f ( x ) = \frac { 1 } { x } - 4$$
 
 A)

Accepted Answer

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

Question 10

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$
-$$f ( x ) = ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $y = x ^ { 16 }$ 
B)  $y = x ^ { 2 }$ 
C)  $y = x ^ { 8 }$ 
D)  $y = x ^ { 64 }$ 
A)  $y = x ^ { 16 }$ 
B)  $y = x ^ { 2 }$ 
C)  $y = x ^ { 8 }$ 
D)  $y = x ^ { 64 }$

Question 11

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$$

Accepted Answer

A)  above the $x$-axis: $( - 4,2 )$
below the x-axis: $( - \infty , - 4 ) , ( 2 , \infty )$ 
B)  above the $x$-axis: no intervals
below the x-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$ 
C)  above the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$
below the $x$-axis: no intervals 
D)  above the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$
below the x-axis: $( - 4,2 )$ 
A)  above the $x$-axis: $( - 4,2 )$
below the x-axis: $( - \infty , - 4 ) , ( 2 , \infty )$ 
B)  above the $x$-axis: no intervals
below the x-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$ 
C)  above the $x$-axis: $( - \infty , - 4 ) , ( - 4,2 ) , ( 2 , \infty )$
below the $x$-axis: no intervals 
D)  above the $x$-axis: $( - \infty , - 4 ) , ( 2 , \infty )$
below the x-axis: $( - 4,2 )$

Question 12

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
-$f ( x ) = 1 + \frac { 6 } { x }$

Accepted Answer

A)  Yes; degree 0 
B)  Yes; degree 6 
C)  Yes; degree 1 
D)  No; x is raised to a negative power 
A)  Yes; degree 0 
B)  Yes; degree 6 
C)  Yes; degree 1 
D)  No; x is raised to a negative power

Question 13

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$
-$$f ( x ) = 3 x - x ^ { 3 }$$

Accepted Answer

A)  $y = x ^ { 2 }$ 
B)  $y = x ^ { 4 }$ 
C)  $y = x ^ { 3 }$ 
D)  $y = - x ^ { 3 }$ 
A)  $y = x ^ { 2 }$ 
B)  $y = x ^ { 4 }$ 
C)  $y = x ^ { 3 }$ 
D)  $y = - x ^ { 3 }$

Question 14

Solve the inequality.
-$$\frac { x - 3 } { x + 7 } < 1$$

Accepted Answer

A)  $( - 7 , \infty )$ 
B)  $( - 7,3 )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - \infty , - 7 )$ or $( 3 , \infty )$ 
A)  $( - 7 , \infty )$ 
B)  $( - 7,3 )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - \infty , - 7 )$ or $( 3 , \infty )$

Question 15

Solve the problem.
-The concentration C of a certain drug in a patient's bloodstream is given by $$\frac { 30 t } { t ^ { 2 } + 49 }$$ a) Find the horizontal asymptote of C(t).
b) Using a graphing utility, determine the time at which the concentration is highest.

Accepted Answer

The answer of Solve the problem.
-The concentration C of a...

Question 16

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

Question 17

Find the indicated intercept(s) of the graph of the function.2133:2139
-$7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

Accepted Answer

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

Question 18

Solve the problem.
-When two lenses are placed next to each other, their combined focal length (a measurement that can be negative or
positive) is described by the equation $$\mathrm { f } = \frac { \mathrm { f } _ { 1 } \mathrm { f } _ { 2 } } { \mathrm { f } _ { 1 } + \mathrm { f } _ { 2 } }$$ If $$\mathrm { f } _ { 1 } = 0.001$$ 01, what are the asymptotes of this function?

Accepted Answer

The answer of Solve the problem.
-When two lenses are placed...

Question 19

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

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } + 100$ 
B)  $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 29 x ^ { 2 } + 100$ 
C)  $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } - 5 x + 100$ 
D)  $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 100$ 
A)  $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } + 100$ 
B)  $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 29 x ^ { 2 } + 100$ 
C)  $f ( x ) = x ^ { 4 } + 29 x ^ { 2 } - 5 x + 100$ 
D)  $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 100$

Question 20

Find the vertical asymptotes of the rational function.
-$$R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }$$

Accepted Answer

A)  $x = - 36$ 
B)  $x = - 12 , x = 3 , x = - 3$ 
C)  $x = - 12 , x = 3$ 
D)  $x = 12 , x = - 3$ 
A)  $x = - 36$ 
B)  $x = - 12 , x = 3 , x = - 3$ 
C)  $x = - 12 , x = 3$ 
D)  $x = 12 , x = - 3$

Solve the equation in the real number system. - $x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree 3: zeros: $1 + i$ and $- 9$

Give the equation of the horizontal asymptote, if any, of the function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 22 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 5 x + 7 x ^ { 3 }$

Use the graph to find the oblique asymptote, if any, of the function. -A) y = -x B) y = x + 1 C) y = x D) no oblique asymptote

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

Find the domain of the rational function. - $f ( x ) = \frac { x ( x - 1 ) } { 16 x ^ { 2 } + 24 x + 5 }$

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = ( x + 8 ) ^ { 2 }$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x - 2 ) ^ { 2 } ( x + 4 ) ^ { 2 }$

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = 1 + \frac { 6 } { x }$

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = 3 x - x ^ { 3 }$

Solve the inequality. - $\frac { x - 3 } { x + 7 } < 1$

Solve the problem. -The concentration C of a certain drug in a patient's bloodstream is given by $\frac { 30 t } { t ^ { 2 } + 49 }$ a) Find the horizontal asymptote of C(t). b) Using a graphing utility, determine the time at which the concentration is highest.

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

Find the indicated intercept(s) of the graph of the function.2133:2139 - $7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

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

Find the vertical asymptotes of the rational function. - $R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 36 }$

Functions and Their Graphs

Linear and Quadratic Functions

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Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

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Sequences; Induction; the Binomial Theorem

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Exam 3: Polynomial and Rational Functions

Solve the equation in the real number system. - x4−8x3+16x2+8x−17=0x ^ { 4 } - 8 x ^ { 3 } + 16 x ^ { 2 } + 8 x - 17 = 0x4−8x3+16x2+8x−17=0

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree 3: zeros: 1+i1 + i1+i and −9- 9−9

Use transformations of the graph o y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 to graph the function. - f(x)=(x+3)4f(x)=(x+3)^{4}f(x)=(x+3)4 A) B) C) D)

Give the equation of the horizontal asymptote, if any, of the function. - R(x)=−3x2x2+9x−22R ( x ) = \frac { - 3 x ^ { 2 } } { x ^ { 2 } + 9 x - 22 }R(x)=x2+9x−22−3x2​

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)=5x+7x3f ( x ) = 5 x + 7 x ^ { 3 }f(x)=5x+7x3