Question 1

Graph the polynomial function.
-$$f ( x ) = - 2 x ( x + 1 ) ^ { 3 }$$

Accepted Answer

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

Question 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 11 ( x - 3 ) ^ { 2 } + 8$$

Accepted Answer

A)  $( 3,8 )$ 
B)  $( 11,3 )$ 
C)  $( - 3,8 )$ 
D)  $( 8 , - 3 )$ 
A)  $( 3,8 )$ 
B)  $( 11,3 )$ 
C)  $( - 3,8 )$ 
D)  $( 8 , - 3 )$

Question 3

Find the y-intercept of the polynomial function.
-

Accepted Answer

A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither

Question 4

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 2 x + 8$$

Accepted Answer

A)  $( 0,8 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0 , - 8 )$ 
A)  $( 0,8 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 4 )$ 
D)  $( 0 , - 8 )$

Question 5

Solve the problem.
-A company that produces computer printers has costs given by the function $C ( x ) = 25 x + 15,000$, 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
$$\bar { C } ( x ) = \frac { 25 x + 15,000 } { x } .$$
What is the horizontal asymptote for the function $\overline { \mathrm { C } }$ ? Describe what this means in practical terms.

Accepted Answer

A)  $\mathrm { y } = 25$; $\$ 25$ is the least possible cost for producing each computer printer. 
B)  $\mathrm { y } = 15,000 ; 15,000$ is the maximum number of computer printers the company can produce. 
C)  $\mathrm { y } = 25 ; 25$ is the minimum number of computer printers the company can produce. 
D)  $y = 15,000$; $\$ 15,000$ is the least possible cost for running the company. 
A)  $\mathrm { y } = 25$; $\$ 25$ is the least possible cost for producing each computer printer. 
B)  $\mathrm { y } = 15,000 ; 15,000$ is the maximum number of computer printers the company can produce. 
C)  $\mathrm { y } = 25 ; 25$ is the minimum number of computer printers the company can produce. 
D)  $y = 15,000$; $\$ 15,000$ is the least possible cost for running the company.

Question 6

Determine the constant of variation for the stated condition.
-$t$ varies directly as $\mathrm { r }$ and inversely as $\mathrm { s }$, and $\mathrm { t } = 2$ when $\mathrm { r } = 30$ and $\mathrm { s } = 75$.

Accepted Answer

A)  $k = 5$ 
B)  $\mathrm { k } = \frac { 1 } { 5 }$ 
C)  $\mathrm { k } = \frac { 2 } { 5 }$ 
D)  $\mathrm { k } = 15$ 
A)  $k = 5$ 
B)  $\mathrm { k } = \frac { 1 } { 5 }$ 
C)  $\mathrm { k } = \frac { 2 } { 5 }$ 
D)  $\mathrm { k } = 15$

Question 7

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } - 1 \right)$$

Accepted Answer

A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither

Question 8

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$16 x ^ { 3 } + 48 x ^ { 2 } - 25 x - 75 > 0$$

Accepted Answer

A)  $\left( - 3 , - \frac { 5 } { 4 } \right) \cup \left( \frac { 5 } { 4 } , \infty \right)$
  
B)  $\left( \frac { 5 } { 4 } , \infty \right)$
  
C)  $( - \infty , - 3 ) \cup \left( - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right)$
  
D)  $( - \infty , - 3 ] \cup \left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
  
A)  $\left( - 3 , - \frac { 5 } { 4 } \right) \cup \left( \frac { 5 } { 4 } , \infty \right)$
  
B)  $\left( \frac { 5 } { 4 } , \infty \right)$
  
C)  $( - \infty , - 3 ) \cup \left( - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right)$
  
D)  $( - \infty , - 3 ] \cup \left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$

Question 9

Find the horizontal asymptote, if any, of the graph of the rational function.
-$$h ( x ) = \frac { - 4 x + 1 } { 5 x + 4 }$$

Accepted Answer

A)  $y = - \frac { 4 } { 5 }$ 
B)  $y = \frac { 1 } { 4 }$ 
C)  $\mathrm { y } = - 4$ 
D)  no horizontal asymptote 
A)  $y = - \frac { 4 } { 5 }$ 
B)  $y = \frac { 1 } { 4 }$ 
C)  $\mathrm { y } = - 4$ 
D)  no horizontal asymptote

Question 10

Find an nth degree polynomial function with real coefficients satisfying the given conditions.
-$\mathrm { n } = 3 ; 3$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( 2 ) = 30$

Accepted Answer

A)  $f ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } - 6 x + 18$ 
B)  $f ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } + 6 x - 18$ 
C)  $f ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } - 6 x + 18$ 
D)  $f ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } + 6 x - 18$ 
A)  $f ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } - 6 x + 18$ 
B)  $f ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } + 6 x - 18$ 
C)  $f ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } - 6 x + 18$ 
D)  $f ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } + 6 x - 18$

Question 11

Divide using synthetic division.
-$$\frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 5 x - 8 } { x - 1 }$$

Accepted Answer

A)  $x ^ { 3 } - 2 x ^ { 2 } - x + 4 - \frac { 4 } { x - 1 }$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + x + 6 + \frac { 8 } { x - 1 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } - x + 6 - \frac { 4 } { x - 1 }$ 
D)  $x ^ { 3 } - 2 x ^ { 2 } + x + 4 + \frac { 8 } { x - 1 }$ 
A)  $x ^ { 3 } - 2 x ^ { 2 } - x + 4 - \frac { 4 } { x - 1 }$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + x + 6 + \frac { 8 } { x - 1 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } - x + 6 - \frac { 4 } { x - 1 }$ 
D)  $x ^ { 3 } - 2 x ^ { 2 } + x + 4 + \frac { 8 } { x - 1 }$

Question 12

Graph the polynomial function.
-$$f ( x ) = ( x - 5 ) ( x - 3 ) ( x - 1 )$$

Accepted Answer

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

Question 13

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { - x + 8 } { x - 2 } \geq 0$$

Accepted Answer

A)  $( 2,8 ]$
  
B)  $( - \infty , 2 )$ or $[ 8 , \infty )$
  
C)  $[ 2,8 ]$
  
D)  $( - \infty , 8 ]$
  
A)  $( 2,8 ]$
  
B)  $( - \infty , 2 )$ or $[ 8 , \infty )$
  
C)  $[ 2,8 ]$
  
D)  $( - \infty , 8 ]$

Question 14

Determine whether the function is a polynomial function.
-$$f ( x ) = 3 x + 7 x ^ { 2 }$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 15

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = - 8 x ^ { 3 } - 3 x ^ { 2 } + 4 x + 3$$

Accepted Answer

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

Question 16

Graph the polynomial function.
-$$f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
-$$f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , touches the $x$-axis and turns around 
B)  $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , crosses the $x$-axis 
C)  1 , crosses the x-axis;
$- 9$, crosses the $x$-axis;
$- 1$, touches the $x$-axis and turns around 
D)  1 , crosses the x-axis;
$- 9$, touches the $x$-axis and turns around;
$- 1$, touches the $x$-axis and turns around 
A)  $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , touches the $x$-axis and turns around 
B)  $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , crosses the $x$-axis 
C)  1 , crosses the x-axis;
$- 9$, crosses the $x$-axis;
$- 1$, touches the $x$-axis and turns around 
D)  1 , crosses the x-axis;
$- 9$, touches the $x$-axis and turns around;
$- 1$, touches the $x$-axis and turns around

Question 19

Find the y-intercept of the polynomial function.
-$$f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$$

Accepted Answer

A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither

Question 20

Determine the constant of variation for the stated condition.
-$y = 5$ when $x = \frac { 1 } { 4 }$

Accepted Answer

A)  $y = 20 x$ 
B)  $y = \frac { 1 } { 20 } x$ 
C)  $y = x + \frac { 19 } { 4 }$ 
D)  $y = \frac { 1 } { 5 } x$ 
A)  $y = 20 x$ 
B)  $y = \frac { 1 } { 20 } x$ 
C)  $y = x + \frac { 19 } { 4 }$ 
D)  $y = \frac { 1 } { 5 } x$

Graph the polynomial function. - $f ( x ) = - 2 x ( x + 1 ) ^ { 3 }$ $Graph the polynomial function. - f ( x ) = - 2 x ( x + 1 ) ^ { 3 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 3 ) ^ { 2 } + 8$

Find the y-intercept of the polynomial function. -

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 2 x + 8$

Determine the constant of variation for the stated condition. - $t$ varies directly as $\mathrm { r }$ and inversely as $\mathrm { s }$ , and $\mathrm { t } = 2$ when $\mathrm { r } = 30$ and $\mathrm { s } = 75$ .

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } - 1 \right)$

Find the horizontal asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { - 4 x + 1 } { 5 x + 4 }$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; 3$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( 2 ) = 30$

Divide using synthetic division. - $\frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 5 x - 8 } { x - 1 }$

Graph the polynomial function. - $f ( x ) = ( x - 5 ) ( x - 3 ) ( x - 1 )$

Determine whether the function is a polynomial function. - $f ( x ) = 3 x + 7 x ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - 8 x ^ { 3 } - 3 x ^ { 2 } + 4 x + 3$

Graph the polynomial function. - $f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$ $Graph the polynomial function. - f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$

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

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

Determine the constant of variation for the stated condition. - $y = 5$ when $x = \frac { 1 } { 4 }$

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

Graph the polynomial function. - f(x)=−2x(x+1)3f ( x ) = - 2 x ( x + 1 ) ^ { 3 }f(x)=−2x(x+1)3

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=11(x−3)2+8f ( x ) = 11 ( x - 3 ) ^ { 2 } + 8f(x)=11(x−3)2+8

Find the y-intercept of the polynomial function. -

Find the y-intercept for the graph of the quadratic function. - f(x)=−x2−2x+8f ( x ) = - x ^ { 2 } - 2 x + 8f(x)=−x2−2x+8

Determine the constant of variation for the stated condition. - ttt varies directly as r\mathrm { r }r and inversely as s\mathrm { s }s , and t=2\mathrm { t } = 2t=2 when r=30\mathrm { r } = 30r=30 and s=75\mathrm { s } = 75s=75 .

Find the y-intercept of the polynomial function. - f(x)=−x2(x+4)(x2−1)f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+4)(x2−1)

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - 16x3+48x2−25x−75>016 x ^ { 3 } + 48 x ^ { 2 } - 25 x - 75 > 016x3+48x2−25x−75>0

Find the horizontal asymptote, if any, of the graph of the rational function. - h(x)=−4x+15x+4h ( x ) = \frac { - 4 x + 1 } { 5 x + 4 }h(x)=5x+4−4x+1​

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - n=3;3\mathrm { n } = 3 ; 3n=3;3 and i\mathrm { i }i are zeros; f(2)=30\mathrm { f } ( 2 ) = 30f(2)=30

Divide using synthetic division. - x4−3x3+x2+5x−8x−1\frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 5 x - 8 } { x - 1 }x−1x4−3x3+x2+5x−8​

Graph the polynomial function. - f(x)=(x−5)(x−3)(x−1)f ( x ) = ( x - 5 ) ( x - 3 ) ( x - 1 )f(x)=(x−5)(x−3)(x−1)

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - −x+8x−2≥0\frac { - x + 8 } { x - 2 } \geq 0x−2−x+8​≥0

Determine whether the function is a polynomial function. - f(x)=3x+7x2f ( x ) = 3 x + 7 x ^ { 2 }f(x)=3x+7x2

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=−8x3−3x2+4x+3f ( x ) = - 8 x ^ { 3 } - 3 x ^ { 2 } + 4 x + 3f(x)=−8x3−3x2+4x+3

Graph the polynomial function. - f(x)=−x2(x−1)(x+3)f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )f(x)=−x2(x−1)(x+3)

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=x−2x2−2x3f ( x ) = x - 2 x ^ { 2 } - 2 x ^ { 3 }f(x)=x−2x2−2x3

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - f(x)=(x+1)(x−9)(x−1)2f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−9)(x−1)2

Find the y-intercept of the polynomial function. - f(x)=(x−4)2(x2−25)f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)f(x)=(x−4)2(x2−25)

Determine the constant of variation for the stated condition. - y=5y = 5y=5 when x=14x = \frac { 1 } { 4 }x=41​

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

Graph the polynomial function. - $f ( x ) = - 2 x ( x + 1 ) ^ { 3 }$ $Graph the polynomial function. - f ( x ) = - 2 x ( x + 1 ) ^ { 3 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 3 ) ^ { 2 } + 8$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } - 2 x + 8$

Determine the constant of variation for the stated condition. - $t$ varies directly as $\mathrm { r }$ and inversely as $\mathrm { s }$ , and $\mathrm { t } = 2$ when $\mathrm { r } = 30$ and $\mathrm { s } = 75$ .

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } - 1 \right)$

Find the horizontal asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { - 4 x + 1 } { 5 x + 4 }$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; 3$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( 2 ) = 30$

Divide using synthetic division. - $\frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 5 x - 8 } { x - 1 }$

Graph the polynomial function. - $f ( x ) = ( x - 5 ) ( x - 3 ) ( x - 1 )$

Determine whether the function is a polynomial function. - $f ( x ) = 3 x + 7 x ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - 8 x ^ { 3 } - 3 x ^ { 2 } + 4 x + 3$

Graph the polynomial function. - $f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$ $Graph the polynomial function. - f ( x ) = - x ^ { 2 } ( x - 1 ) ( x + 3 )$

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

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

Determine the constant of variation for the stated condition. - $y = 5$ when $x = \frac { 1 } { 4 }$