Question 1

Find the domain and range of the quadratic function whose graph is described.
-The vertex is (-1, -12) and the graph opens up.

Accepted Answer

A)  Domain: (-∞, ∞)
Range: [-12, ∞) 
B)  Domain: [-1, ∞)
Range: [-12, ∞) 
C)  Domain: (-∞, ∞)
Range: (-∞, -12] 
D)  Domain: (-∞, ∞)
Range: [-1, ∞) 
A)  Domain: (-∞, ∞)
Range: [-12, ∞) 
B)  Domain: [-1, ∞)
Range: [-12, ∞) 
C)  Domain: (-∞, ∞)
Range: (-∞, -12] 
D)  Domain: (-∞, ∞)
Range: [-1, ∞)

Question 2

Determine the constant of variation for the stated condition.
-The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 28 watts of power when 2 amperes of current is flowing through the resistor whose resistance is 7 ohms, find the power that a resistor needs to dissipate when 3 amperes of current are flowing through a resistor whose resistance is 7 ohms.

Accepted Answer

A)  63 watts 
B)  21 watts 
C)  147 watts 
D)  42 watts 
A)  63 watts 
B)  21 watts 
C)  147 watts 
D)  42 watts

Question 3

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 2 x + 6 }$

Accepted Answer

A)  $( 6,0 )$ 
B)  $( \sqrt { 5 } , 0 ) , ( - \sqrt { 5 } , 0 )$ 
C)  $( 5,0 )$ 
D)  none 
A)  $( 6,0 )$ 
B)  $( \sqrt { 5 } , 0 ) , ( - \sqrt { 5 } , 0 )$ 
C)  $( 5,0 )$ 
D)  none

Question 4

Find the slant asymptote, if any, of the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } + 5 x - 3 } { x - 4 }$$

Accepted Answer

A)  $y = x + 9$ 
B)  $y = x + 5$ 
C)  $y = x$ 
D)  no slant asymptote 
A)  $y = x + 9$ 
B)  $y = x + 5$ 
C)  $y = x$ 
D)  no slant asymptote

Question 5

Solve the problem.
-The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300$. Find the number of pretzels that must be sold to maximize profit.

Accepted Answer

A)  400 pretzels 
B)  800 pretzels 
C)  $0.8$ pretzels 
D)  20 pretzels 
A)  400 pretzels 
B)  800 pretzels 
C)  $0.8$ pretzels 
D)  20 pretzels

Question 6

Determine whether the graph shown is the graph of a polynomial function.
-

Accepted Answer

A)  not a polynomial function 
B)  polynomial function 
A)  not a polynomial function 
B)  polynomial function

Question 7

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } - 5 x ^ { 2 } + 2 x - 5$$

Accepted Answer

A)  rises to the left and rises to the right 
B)  rises to the left and falls to the right 
C)  falls to the left and rises to the right 
D)  falls to the left and falls to the right 
A)  rises to the left and rises to the right 
B)  rises to the left and falls to the right 
C)  falls to the left and rises to the right 
D)  falls to the left and falls to the right

Question 8

Find the y-intercept of the polynomial function.
-$$x ^ { 5 } - 15 x ^ { 3 } + 54 x = 0$$

Accepted Answer

A)  origin symmetry 
B)  $\mathrm { y }$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $\mathrm { y }$-axis symmetry 
C)  neither

Question 9

Solve the problem.
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 528 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area.

Accepted Answer

A)  88 ft by 132 ft 
B)  132 ft by 132 ft 
C)  44 ft by 198 ft 
D)  66 ft by 132 ft 
A)  88 ft by 132 ft 
B)  132 ft by 132 ft 
C)  44 ft by 198 ft 
D)  66 ft by 132 ft

Question 10

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6$$

Accepted Answer

A)  $\{ - 3 , - 1,2 \}$ 
B)  $\{ - 2,1,3 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ - 1 \}$ 
A)  $\{ - 3 , - 1,2 \}$ 
B)  $\{ - 2,1,3 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ - 1 \}$

Question 11

Find the domain of the rational function.
-$$g ( x ) = \frac { 7 x ^ { 2 } } { ( x - 3 ) ( x - 1 ) }$$

Accepted Answer

A)  $\{ x \mid x \neq 3 , x \neq 1 \}$ 
B)  $\{ x \mid x \neq - 3 , x \neq - 1 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq 1 , x \neq - 7 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq 3 , x \neq 1 \}$ 
B)  $\{ x \mid x \neq - 3 , x \neq - 1 \}$ 
C)  $\{ x \mid x \neq 3 , x \neq 1 , x \neq - 7 \}$ 
D)  all real numbers

Question 12

Divide using long division.
-$$\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)$$

Accepted Answer

A)  $3 x + \frac { 1 } { 9 }$ 
B)  $3 x + 9$ 
C)  $3 x + \frac { - 2 } { 9 x ^ { 2 } - 18 }$ 
D)  $3 x + \frac { 2 } { 9 x ^ { 2 } - 18 }$ 
A)  $3 x + \frac { 1 } { 9 }$ 
B)  $3 x + 9$ 
C)  $3 x + \frac { - 2 } { 9 x ^ { 2 } - 18 }$ 
D)  $3 x + \frac { 2 } { 9 x ^ { 2 } - 18 }$

Question 13

Write an equation that expresses the relationship. Use k as the constant of variation.
-$x$ varies inversely as $\mathrm { v }$, and $x = 42$ when $\mathrm { v } = 8$. Find $\mathrm { x }$ when $\mathrm { v } = 48$.

Accepted Answer

A)  $x = 7$ 
B)  $x = 64$ 
C)  $x = 56$ 
D)  $x = 6$ 
A)  $x = 7$ 
B)  $x = 64$ 
C)  $x = 56$ 
D)  $x = 6$

Question 14

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-Touches the $x$-axis at 0 and crosses the $x$-axis at 2 ; lies below the $x$-axis between 0 and 2 .

Accepted Answer

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

Question 15

Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
-$$f ( x ) = - x ^ { 2 } - 2 x - 8$$

Accepted Answer

A)  maximum; $( - 1 , - 7 )$ 
B)  minimum; $( - 1 , - 7 )$ 
C)  minimum; $( - 7 , - 1 )$ 
D)  maximum; $( - 7 , - 1 )$ 
A)  maximum; $( - 1 , - 7 )$ 
B)  minimum; $( - 1 , - 7 )$ 
C)  minimum; $( - 7 , - 1 )$ 
D)  maximum; $( - 7 , - 1 )$

Question 16

Determine the constant of variation for the stated condition.
-$y = 5$ when $x = 15$

Accepted Answer

A)  $y = \frac { 1 } { 3 } x$ 
B)  $y = 3 x$ 
C)  $\mathrm { y } = \mathrm { x } + 10$ 
D)  $y = \frac { 1 } { 5 } x$ 
A)  $y = \frac { 1 } { 3 } x$ 
B)  $y = 3 x$ 
C)  $\mathrm { y } = \mathrm { x } + 10$ 
D)  $y = \frac { 1 } { 5 } x$

Question 17

Determine whether the function is a polynomial function.
-$$f ( x ) = 3 x - x ^ { 4 } + \frac { 3 } { 2 }$$

Accepted Answer

A)  4 
B)  1 
C)  3 
D)  $- 1$ 
A)  4 
B)  1 
C)  3 
D)  $- 1$

Question 18

Solve the problem.
-A company that produces computer printers has costs given by the function $C ( x ) = 30 x + 20,000$, where $x$ is the number of computer printers manufactured and $C ( x )$ is measured in dollars. The average cost to manufacture each computer printer is given by
$$\bar { C } ( x ) = \frac { 30 x + 20,000 } { x }$$
Find $\bar { C } ( 250 )$. (Round to the nearest dollar, if necessary.)

Accepted Answer

A)  $\$ 110$ 
B)  $\$ 90$ 
C)  $\$ 38$ 
D)  $\$ 40$ 
A)  $\$ 110$ 
B)  $\$ 90$ 
C)  $\$ 38$ 
D)  $\$ 40$

Question 19

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$x ^ { 2 } + 7 x \geq 0$$

Accepted Answer

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

Question 20

Solve the problem.
-You have 136 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Accepted Answer

A)  34 ft by 34 ft 
B)  68 ft by 68 ft 
C)  68 ft by 17 ft 
D)  36 ft by 32 ft 
A)  34 ft by 34 ft 
B)  68 ft by 68 ft 
C)  68 ft by 17 ft 
D)  36 ft by 32 ft

Find the domain and range of the quadratic function whose graph is described. -The vertex is (-1, -12) and the graph opens up.

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 2 x + 6 }$

Find the slant asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 5 x - 3 } { x - 4 }$

Solve the problem. -The profit that the vendor makes per day by selling $x$ pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300$ . Find the number of pretzels that must be sold to maximize profit.

Determine whether the graph shown is the graph of a polynomial function. -

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = 4 x ^ { 4 } - 3 x ^ { 3 } - 5 x ^ { 2 } + 2 x - 5$

Find the y-intercept of the polynomial function. - $x ^ { 5 } - 15 x ^ { 3 } + 54 x = 0$

Solve the problem. -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 528 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area.

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 5 x - 6$

Find the domain of the rational function. - $g ( x ) = \frac { 7 x ^ { 2 } } { ( x - 3 ) ( x - 1 ) }$

Divide using long division. - $\left( 27 x ^ { 3 } + x ^ { 2 } - 54 x - 2 \right) \div \left( 9 x ^ { 2 } - 18 \right)$

Write an equation that expresses the relationship. Use k as the constant of variation. - $x$ varies inversely as $\mathrm { v }$ , and $x = 42$ when $\mathrm { v } = 8$ . Find $\mathrm { x }$ when $\mathrm { v } = 48$ .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 2 ; lies below the $x$ -axis between 0 and 2 .

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = - x ^ { 2 } - 2 x - 8$

Determine the constant of variation for the stated condition. - $y = 5$ when $x = 15$

Determine whether the function is a polynomial function. - $f ( x ) = 3 x - x ^ { 4 } + \frac { 3 } { 2 }$

Solve the problem. -You have 136 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 3: Polynomial and Rational Functions

Find the domain and range of the quadratic function whose graph is described. -The vertex is (-1, -12) and the graph opens up.

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=x2+5x2+2x+6f ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 2 x + 6 }f(x)=x2+2x+6x2+5​

Find the slant asymptote, if any, of the graph of the rational function. - f(x)=x2+5x−3x−4f ( x ) = \frac { x ^ { 2 } + 5 x - 3 } { x - 4 }f(x)=x−4x2+5x−3​

Solve the problem. -The profit that the vendor makes per day by selling xxx pretzels is given by the function P(x)=−0.002x2+1.6x−300P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 300P(x)=−0.002x2+1.6x−300 . Find the number of pretzels that must be sold to maximize profit.