Question 1

Determine the maximum possible number of turning points for the graph of the function.
-$f ( x ) = x ^ { 2 } + 6 x ^ { 3 }$

Accepted Answer

A) 2 
B) 3 
C) 1 
D) 6 
A) 2 
B) 3 
C) 1 
D) 6

Question 2

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.
-$f ( x ) = x ^ { 2 } + 8 x - 2 \text { in } ( 0,1 )$

Accepted Answer

A) Yes 
B) Cannot determine 
A) Yes 
B) Cannot determine

Question 3

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = 4 x ^ { 2 } - 4 x - 1 \text { in } [ - 1,2 ]$

Accepted Answer

A) Yes 
B) Cannot determine 
A) Yes 
B) Cannot determine

Question 4

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.
-$f ( x ) = \frac { 5 x ^ { 2 } - 6 x - 5 } { 6 x ^ { 2 } - 7 x + 4 }$

Accepted Answer

A)  $\text { Oblique asymptote: } y = \frac { 5 } { 6 } x + \frac { 5 } { 4 }$ 
B)  $y = \frac { 5 } { 6 }$ 
C) Neither 
A)  $\text { Oblique asymptote: } y = \frac { 5 } { 6 } x + \frac { 5 } { 4 }$ 
B)  $y = \frac { 5 } { 6 }$ 
C) Neither

Question 5

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of
discontinuity.
-$$f ( x ) = 3 ^ { x } - 2$$

Accepted Answer

A) discontinuous at x = 0 
B) continuous 
C) discontinuous at x = -2 
D) discontinuous at x = 2 
A) discontinuous at x = 0 
B) continuous 
C) discontinuous at x = -2 
D) discontinuous at x = 2

Question 6

Determine the maximum possible number of turning points for the graph of the function.
-$f ( x ) = ( x + 2 ) ( x - 4 ) ( 4 x - 6 )$

Accepted Answer

A) 3 
B) 4 
C) 0 
D) 2 
A) 3 
B) 4 
C) 0 
D) 2

Question 7

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }$

Accepted Answer

A) 4: vertical asymptote 
B) -4: vertical asymptote 
C) 3: vertical asymptote; -3: vertical asymptote 
D) no points of discontinuity 
A) 4: vertical asymptote 
B) -4: vertical asymptote 
C) 3: vertical asymptote; -3: vertical asymptote 
D) no points of discontinuity

Question 8

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.
-$f ( x ) = \frac { 8 x ^ { 2 } - 1 } { 16 x ^ { 3 } - 1 }$

Accepted Answer

A)  $y = \frac { x } { 2 } - 1$ 
B) Horizontal asymptote: y = 0 
C) Neither 
A)  $y = \frac { x } { 2 } - 1$ 
B) Horizontal asymptote: y = 0 
C) Neither

Question 9

Solve the problem.
-Given $R ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x$ and $C ( x ) = 2 x ^ { 2 } + 24$ where $x$ represents the number of items produced in hundreds, $R( \mathrm { x } )$ and $\mathrm { C } ( \mathrm { x } )$ represent revenue and cost in thousands of dollars. where x represents the number of items produced in hundreds, R(x)
a)Find P(x).
b)Find P(0), R(0), and C(0)and interpret each of these.
c)Find the break-even point (value wherehere $P ( x ) = 0 ) \text { if } 0  0 \text { if } 0 < x < 4 ?$ e)For what values of x ist values of x is $P ( x ) < 0 \text { if } 0 < x < 4 ?$ f)Interpret the results from parts d)and e).

Accepted Answer

a) @#IMG-DLM& b)P(0)= -24, the company lost $24,00

Question 10

Solve the problem.
-Sam Wright wants to stock up on cans of cat food which are selling for $0.95 per can. Write a greatest integer function that represents the number of cans he can purchase with x dollars.

Accepted Answer

A)  $f ( x ) = 0.95 \llbracket x \rrbracket$ 
B)  $f ( x ) = \llbracket 0.95 x \rrbracket$ 
C)  $f ( x ) = \llbracket \frac { x } { 0.95 } \rrbracket$ 
D)  $f ( x ) = \frac { \llbracket x \rrbracket } { 0.95 }$ 
A)  $f ( x ) = 0.95 \llbracket x \rrbracket$ 
B)  $f ( x ) = \llbracket 0.95 x \rrbracket$ 
C)  $f ( x ) = \llbracket \frac { x } { 0.95 } \rrbracket$ 
D)  $f ( x ) = \frac { \llbracket x \rrbracket } { 0.95 }$

Question 11

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }$

Accepted Answer

A) -7: hole; -8: vertical asymptote 
B) -7: hole; -9: vertical asymptote 
C) -8: vertical asymptote 
D) 7: hole; 8: vertical asymptote 
A) -7: hole; -8: vertical asymptote 
B) -7: hole; -9: vertical asymptote 
C) -8: vertical asymptote 
D) 7: hole; 8: vertical asymptote

Question 12

Find all real zeros (estimate the irrational zeros to the nearest hundredth).
-$f ( x ) = 3 x ^ { 3 } - 18 x ^ { 2 } + 5 x - 30$

Accepted Answer

A) 6, -1.29, 1.29 
B) 6 
C) -1.29, 1.29 
D) 1.29, 6 
A) 6, -1.29, 1.29 
B) 6 
C) -1.29, 1.29 
D) 1.29, 6

Question 13

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 18 \text { in } [ - 3,3 ]$

Accepted Answer

A) Yes 
B) Cannot determine 
A) Yes 
B) Cannot determine

Question 14

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = 5 ( x + 3 ) ( x + 7 ) ^ { 4 }$

Accepted Answer

A) x = 3, x = 4 
B) x = -3, x = 4 
C)  $\begin{array} { l } 
x = 3 \
x = 7 , \text { multiplicity: } 4 \
x = 4
\end{array}$ 
D)  $\begin{array} { l } 
x = - 3 \
x = - 7 , \text { multiplicity: } 4
\end{array}$ 
A) x = 3, x = 4 
B) x = -3, x = 4 
C)  $\begin{array} { l } 
x = 3 \
x = 7 , \text { multiplicity: } 4 \
x = 4
\end{array}$ 
D)  $\begin{array} { l } 
x = - 3 \
x = - 7 , \text { multiplicity: } 4
\end{array}$

Question 15

Graph the polynomial function.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6$

Accepted Answer

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

Question 16

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x - 8 } { x ^ { 2 } - 16 }$

Accepted Answer

A) -4: vertical asymptote 
B) 8: vertical asymptote 
C) 4: vertical asymptote; -4: vertical asymptote 
D) 4: vertical asymptote 
A) -4: vertical asymptote 
B) 8: vertical asymptote 
C) 4: vertical asymptote; -4: vertical asymptote 
D) 4: vertical asymptote

Question 17

Determine the minimum degree of the polynomial function graphed.
-$f ( x ) = ( x - 4 ) ( x - 2 ) ( x + 1 ) ( x + 2 )$

Accepted Answer

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

Question 18

Find all the zeros (real and complex)of the function.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

Accepted Answer

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

Question 19

Classify the function as continuous or discontinuous.
-

Accepted Answer

A) discontinuous 
B) continuous 
A) discontinuous 
B) continuous

Question 20

Find the x-intercepts of the function.
-$f ( x ) = 4 x ^ { 2 } - 44$

Accepted Answer

A) x-intercept: (12, 0) 
B)  $x \text {-intercept: } ( \sqrt { 11 } , 0 )$ 
C) x-intercept: (-11, 0), x-intercept: (11, 0) 
D)  $x \text {-intercept: } ( - \sqrt { 11 } , 0 ) , x \text {-intercept: } ( \sqrt { 11 } , 0 )$ 
A) x-intercept: (12, 0) 
B)  $x \text {-intercept: } ( \sqrt { 11 } , 0 )$ 
C) x-intercept: (-11, 0), x-intercept: (11, 0) 
D)  $x \text {-intercept: } ( - \sqrt { 11 } , 0 ) , x \text {-intercept: } ( \sqrt { 11 } , 0 )$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 2 } + 6 x ^ { 3 }$

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. - $f ( x ) = x ^ { 2 } + 8 x - 2 \text { in } ( 0,1 )$

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - $f ( x ) = 4 x ^ { 2 } - 4 x - 1 \text { in } [ - 1,2 ]$

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. - $f ( x ) = \frac { 5 x ^ { 2 } - 6 x - 5 } { 6 x ^ { 2 } - 7 x + 4 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = 3 ^ { x } - 2$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x + 2 ) ( x - 4 ) ( 4 x - 6 )$

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }$

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. - $f ( x ) = \frac { 8 x ^ { 2 } - 1 } { 16 x ^ { 3 } - 1 }$

Solve the problem. -Sam Wright wants to stock up on cans of cat food which are selling for $0.95 per can. Write a greatest integer function that represents the number of cans he can purchase with x dollars.

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }$

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - $f ( x ) = 3 x ^ { 3 } - 18 x ^ { 2 } + 5 x - 30$

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 18 \text { in } [ - 3,3 ]$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 5 ( x + 3 ) ( x + 7 ) ^ { 4 }$

Graph the polynomial function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6$ $Graph the polynomial function. - f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6$

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x - 8 } { x ^ { 2 } - 16 }$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = ( x - 4 ) ( x - 2 ) ( x + 1 ) ( x + 2 )$

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

Classify the function as continuous or discontinuous. -

Find the x-intercepts of the function. - $f ( x ) = 4 x ^ { 2 } - 44$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and Probability

Filters

Exam 10: Characteristics of Functions and Their Graphs

Determine the maximum possible number of turning points for the graph of the function. - f(x)=x2+6x3f ( x ) = x ^ { 2 } + 6 x ^ { 3 }f(x)=x2+6x3

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)=x2+8x−2 in (0,1)f ( x ) = x ^ { 2 } + 8 x - 2 \text { in } ( 0,1 )f(x)=x2+8x−2 in (0,1)

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - f(x)=4x2−4x−1 in [−1,2]f ( x ) = 4 x ^ { 2 } - 4 x - 1 \text { in } [ - 1,2 ]f(x)=4x2−4x−1 in [−1,2]

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)=5x2−6x−56x2−7x+4f ( x ) = \frac { 5 x ^ { 2 } - 6 x - 5 } { 6 x ^ { 2 } - 7 x + 4 }f(x)=6x2−7x+45x2−6x−5​

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - f(x)=3x−2f ( x ) = 3 ^ { x } - 2f(x)=3x−2

Determine the maximum possible number of turning points for the graph of the function. - f(x)=(x+2)(x−4)(4x−6)f ( x ) = ( x + 2 ) ( x - 4 ) ( 4 x - 6 )f(x)=(x+2)(x−4)(4x−6)

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - f(x)=x−9x2+4f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }f(x)=x2+4x−9​

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)=8x2−116x3−1f ( x ) = \frac { 8 x ^ { 2 } - 1 } { 16 x ^ { 3 } - 1 }f(x)=16x3−18x2−1​

Solve the problem. -Sam Wright wants to stock up on cans of cat food which are selling for $0.95 per can. Write a greatest integer function that represents the number of cans he can purchase with x dollars.

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - f(x)=x2+16x+63x2+15x+56f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }f(x)=x2+15x+56x2+16x+63​

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - f(x)=3x3−18x2+5x−30f ( x ) = 3 x ^ { 3 } - 18 x ^ { 2 } + 5 x - 30f(x)=3x3−18x2+5x−30

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - f(x)=x3−3x2−5x+18 in [−3,3]f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 18 \text { in } [ - 3,3 ]f(x)=x3−3x2−5x+18 in [−3,3]

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x)=5(x+3)(x+7)4f ( x ) = 5 ( x + 3 ) ( x + 7 ) ^ { 4 }f(x)=5(x+3)(x+7)4

Graph the polynomial function. - f(x)=x3+2x2+x−6f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6f(x)=x3+2x2+x−6

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - f(x)=x−8x2−16f ( x ) = \frac { x - 8 } { x ^ { 2 } - 16 }f(x)=x2−16x−8​

Determine the minimum degree of the polynomial function graphed. - f(x)=(x−4)(x−2)(x+1)(x+2)f ( x ) = ( x - 4 ) ( x - 2 ) ( x + 1 ) ( x + 2 )f(x)=(x−4)(x−2)(x+1)(x+2)

Find all the zeros (real and complex)of the function. - f(x)=x3+2x2−6x+8f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8f(x)=x3+2x2−6x+8

Classify the function as continuous or discontinuous. -

Find the x-intercepts of the function. - f(x)=4x2−44f ( x ) = 4 x ^ { 2 } - 44f(x)=4x2−44

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and Probability

Filters

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 2 } + 6 x ^ { 3 }$

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. - $f ( x ) = x ^ { 2 } + 8 x - 2 \text { in } ( 0,1 )$

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - $f ( x ) = 4 x ^ { 2 } - 4 x - 1 \text { in } [ - 1,2 ]$

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. - $f ( x ) = \frac { 5 x ^ { 2 } - 6 x - 5 } { 6 x ^ { 2 } - 7 x + 4 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = 3 ^ { x } - 2$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x + 2 ) ( x - 4 ) ( 4 x - 6 )$

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }$

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. - $f ( x ) = \frac { 8 x ^ { 2 } - 1 } { 16 x ^ { 3 } - 1 }$

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }$

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - $f ( x ) = 3 x ^ { 3 } - 18 x ^ { 2 } + 5 x - 30$

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 18 \text { in } [ - 3,3 ]$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 5 ( x + 3 ) ( x + 7 ) ^ { 4 }$

Graph the polynomial function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6$ $Graph the polynomial function. - f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + x - 6$

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x - 8 } { x ^ { 2 } - 16 }$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = ( x - 4 ) ( x - 2 ) ( x + 1 ) ( x + 2 )$

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8$

Find the x-intercepts of the function. - $f ( x ) = 4 x ^ { 2 } - 44$