Question 1

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
-$f ( x ) = \frac { 10 x ^ { 3 } - 17 x ^ { 2 } + 3 x - 1 } { 4 x ^ { 2 } - 1 }$

Accepted Answer

A)  $\text { Oblique asymptote: } y = \frac { 5 } { 2 } x - \frac { 17 } { 4 }$ 
B)  $\text { Horizontal asymptote: } y = \frac { 5 } { 2 }$ 
C) Neither

Question 2

Solve the problem.
-A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a
Paddle boat as a function of hours it is rented.

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 
7 \llbracket  x \rrbracket & \text { if } 0  3
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 
7 \llbracket x \rrbracket & \text { if } 0  3
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 
7 \llbracket x \rrbracket & \text { if } 0  3
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 
7 \llbracket x \rrbracket & \text { if } 0  3
\end{array} \right.$

Question 3

Determine the minimum degree of the polynomial function graphed.
-

Accepted Answer

A) 2 
B) 4 
C) 3 
D) -2

Question 4

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

Accepted Answer

A) 7: vertical asymptote 
B) 5: vertical asymptote 
C) 7: vertical asymptote; 5: vertical asymptote 
D) -7: vertical asymptote; -5: vertical asymptote

Question 5

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Accepted Answer

A) x = 3, x = 4 
B) x = 0, x = 3, x = 4 
C) x = 0, x = - 5, x = 4 
D) x = - 5, x = 4

Question 6

Find the x-intercepts of the function.
-$f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

Accepted Answer

A) x-intercept: (0, 0), x-intercept: (-5, 0) 
B) x-intercept: (0, 0), x-intercept: (5, 0), x-intercept: (-5, 0)x-intercept: (4, 0), x-intercept: (-4, 0) 
C) x-intercept: (0, 0), x-intercept: (5, 0) 
D) x-intercept: (0, 0), x-intercept: (5, 0), x-intercept: (-5, 0)

Question 7

Graph the piecewise function.
-$f ( x ) = \left\{ \begin{array} { l l } 
- 2 x & \text { if } x \leq - 2 \
- 2 x + 2 & \text { if } - 2  2
\end{array} \right.$

Accepted Answer

A)   
B)   
C)   
D)

Question 8

List the possible rational zeros of the function.
-$x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

Accepted Answer

A)  $\pm 7 , \pm \frac { 1 } { 7 }$ 
B)  $\pm \frac { 1 } { 5 } , \pm \frac { 7 } { 5 } , \pm 7$ 
C)  $\pm 1 , \pm 7$ 
D)  $\pm 1 , \pm \frac { 1 } { 7 }$

Question 9

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = x ^ { 2 } - 16 x + 64$

Accepted Answer

A) x = -8, multiplicity: 2 
B) x = 8, multiplicity: 2 
C) x = 16, multiplicity: 2 
D) x = 8, x = -8

Question 10

Find all the zeros (real and complex)of the function.
-$f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

Accepted Answer

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

Question 11

Use the Intermediate Value Theorem to determine if a real zero of f(x)occurs in the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 5 x - 3 \text { in } ( - 1,0 )$

Accepted Answer

A) Cannot determine 
B) Yes

Question 12

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = 2 x ^ { 2 } - 26$

Accepted Answer

A)  $x = \sqrt { 13 } , \text { mutiplicity: } 2$ 
B) x = -13, x = 13 
C)  $x = - \sqrt { 13 } , x = \sqrt { 13 }$ 
D) x = 13, mutiplicity: 2

Question 13

Graph the rational function.
-$f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$

Accepted Answer

A)   
B)   
C)   
D)

Question 14

Graph the piecewise function.
-$f ( x ) = \left\{ \begin{array} { l l } 
x + 5 & \text { if } x > 4 \
- ( x + 5 ) & \text { if } x \leq 4
\end{array} \right.$

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Determine the minimum degree of the polynomial function graphed.
-$f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$

Accepted Answer

A)   
B)   
C)   
D)

Question 16

Find all the zeros (real and complex)of the function.
-$f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

Accepted Answer

A)  $- 2 \mathrm { i } , 2 \mathrm { i } , 8 \mathrm { i } , - 8 \mathrm { i }$ 
B)  $- 2 \mathrm { i } , 2 \mathrm { i } , 4 , - 4$ 
C)  $- 2 \mathrm { i } , 2 \mathrm { i } , 4 \mathrm { i } , - 4 \mathrm { i }$ 
D)  $- 2 \mathrm { i } , 2 \mathrm { i } , 8 , - 8$

Question 17

Determine whether the function is an even function, an odd function, or neither.
-$f ( x ) = x ^ { 5 } - x ^ { 4 }$

Accepted Answer

A) Odd 
B) Even 
C) Neither

Question 18

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph
the function.
-$f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

Accepted Answer

A) maximum number of x-intercepts: 9; minimum number of x-intercepts: 3 
B) maximum number of x-intercepts: 9; minimum number of x-intercepts: 2 
C) maximum number of x-intercepts: 9; minimum number of x-intercepts: 0 
D) maximum number of x-intercepts: 9; minimum number of x-intercepts: 1

Question 19

Use the Intermediate Value Theorem to determine if a real zero of f(x)occurs in the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 4 x ^ { 2 } + 5 x + 2 \text { in } ( 3,4 )$

Accepted Answer

A) Cannot determine 
B) Yes

Question 20

Graph the greatest integer function.
-$f ( x ) = \llbracket x - 2 \rrbracket$

Accepted Answer

A)   
B)   
C)   
D)

Exam 10: Characteristics of Functions and Their Graphs

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - $f ( x ) = \frac { 10 x ^ { 3 } - 17 x ^ { 2 } + 3 x - 1 } { 4 x ^ { 2 } - 1 }$

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented.

Determine the minimum degree of the polynomial function graphed. -

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Find the x-intercepts of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

List the possible rational zeros of the function. - $x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 16 x + 64$

Find all the zeros (real and complex) of the function. - $f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 5 x - 3 \text { in } ( - 1,0 )$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 2 x ^ { 2 } - 26$

Graph the rational function. - $f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 } A) B) C) D)$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 ) A) B) C) D)$

Find all the zeros (real and complex) of the function. - $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 5 } - x ^ { 4 }$

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 4 x ^ { 2 } + 5 x + 2 \text { in } ( 3,4 )$

Graph the greatest integer function. - $f ( x ) = \llbracket x - 2 \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket x - 2 \rrbracket A) B) C) D)$

Exam 10: Characteristics of Functions and Their Graphs

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented.

Determine the minimum degree of the polynomial function graphed. -

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - f(x) =x2+12x+35x2−12x+35f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }f(x) =x2−12x+35x2+12x+35​

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x) =x3+x2−20xf ( x ) = x ^ { 3 } + x ^ { 2 } - 20 xf(x) =x3+x2−20x

Find the x-intercepts of the function. - f(x) =x5(x2−25) (x2+16) f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right) f(x) =x5(x2−25) (x2+16)

List the possible rational zeros of the function. - x5−5x2+5x+7x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7x5−5x2+5x+7

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x) =x2−16x+64f ( x ) = x ^ { 2 } - 16 x + 64f(x) =x2−16x+64

Find all the zeros (real and complex) of the function. - f(x) =3x4−23x3+89x2−167x+78f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78f(x) =3x4−23x3+89x2−167x+78

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x) =2x2−26f ( x ) = 2 x ^ { 2 } - 26f(x) =2x2−26

Graph the rational function. - f(x) =x3+2x2+4x+8x+2f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }f(x) =x+2x3+2x2+4x+8​

Graph the piecewise function. - f(x) ={x+5 if x>4−(x+5) if x≤4f ( x ) = \left\{ \begin{array} { l l } x + 5 & \text { if } x > 4 \\- ( x + 5 ) & \text { if } x \leq 4\end{array} \right.f(x) ={x+5−(x+5) ​ if x>4 if x≤4​

Determine the minimum degree of the polynomial function graphed. - f(x) =x2(x−5) (x−1) f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 ) f(x) =x2(x−5) (x−1)

Find all the zeros (real and complex) of the function. - f(x) =x4−12x2−64f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64f(x) =x4−12x2−64

Determine whether the function is an even function, an odd function, or neither. - f(x) =x5−x4f ( x ) = x ^ { 5 } - x ^ { 4 }f(x) =x5−x4

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - f(x) =5x9−4x8+x7+2.5x+15f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15f(x) =5x9−4x8+x7+2.5x+15

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - f(x) =x4+4x3−4x2+5x+2 in (3,4) f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 4 x ^ { 2 } + 5 x + 2 \text { in } ( 3,4 ) f(x) =x4+4x3−4x2+5x+2 in (3,4)

Graph the greatest integer function. - f(x) =⟦x−2⟧f ( x ) = \llbracket x - 2 \rrbracketf(x) =[[x−2]]

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Find the x-intercepts of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

List the possible rational zeros of the function. - $x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 16 x + 64$

Find all the zeros (real and complex) of the function. - $f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 2 x ^ { 2 } - 26$

Graph the rational function. - $f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 } A) B) C) D)$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 ) A) B) C) D)$

Find all the zeros (real and complex) of the function. - $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 5 } - x ^ { 4 }$

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 4 x ^ { 2 } + 5 x + 2 \text { in } ( 3,4 )$

Graph the greatest integer function. - $f ( x ) = \llbracket x - 2 \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket x - 2 \rrbracket A) B) C) D)$