Question 1

Use the remainder theorem and synthetic division to find f(k).
-$$k = 5 ; f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 2$$

Accepted Answer

A)  -218 
B)  28 
C)  32 
D)  -220 
A)  -218 
B)  28 
C)  32 
D)  -220

Question 2

Use the remainder theorem and synthetic division to find f(k).
-$$k = 4 ; f ( x ) = 4 x ^ { 4 } + 3 x ^ { 3 } + 3 x ^ { 2 } - 6 x + 22$$

Accepted Answer

A)  1976 
B)  1262 
C)  786 
D)  5054 
A)  1976 
B)  1262 
C)  786 
D)  5054

Question 3

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $- \frac { 2 } { 3 }$ 
B)  16 
C)  $\frac { 16 } { 3 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $- \frac { 2 } { 3 }$ 
B)  16 
C)  $\frac { 16 } { 3 }$ 
D)  $\frac { 2 } { 3 }$

Question 4

Find an equation for the rational function graph.
-Suppose a cost-benefit model is given by $\mathrm { f } ( \mathrm { x } ) = \frac { 4.3 \mathrm { x } } { 100 - \mathrm { x } }$, where $\mathrm { y }$ is the cost in thousands of dollars for removing $x$ percent of a given pollutant. Find the cost of removing $60 \%$ to the nearest dollar.

Accepted Answer

A)  $\$ 4300$ 
B)  $\$ 6450$ 
C)  $\$ 1500$ 
D)  $\$ 2580$ 
A)  $\$ 4300$ 
B)  $\$ 6450$ 
C)  $\$ 1500$ 
D)  $\$ 2580$

Question 5

Round to the nearest tenth unless indicated otherwise.
-Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of $50 \mathrm { mph }$ with a surface area of $36 \mathrm { ft } ^ { 2 }$ experiences a drag of $270 \mathrm {~N}$ (Newtons), how fast must a car with $35 \mathrm { ft } ^ { 2 }$ of surface area travel in order to experience a drag force of $231 \mathrm {~N}$ ?

Accepted Answer

A)  $49 \mathrm { mph }$ 
B)  $46 \mathrm { mph }$ 
C)  $41 \mathrm { mph }$ 
D)  $44 \mathrm { mph }$ 
A)  $49 \mathrm { mph }$ 
B)  $46 \mathrm { mph }$ 
C)  $41 \mathrm { mph }$ 
D)  $44 \mathrm { mph }$

Question 6

Identify the vertex of the parabola.
-$$y = 3 x ^ { 2 } + 12 x + 17$$

Accepted Answer

A)  $( 5 , - 2 )$ 
B)  $( - 5,2 )$ 
C)  $( 2 , - 5 )$ 
D)  $( - 2,5 )$ 
A)  $( 5 , - 2 )$ 
B)  $( - 5,2 )$ 
C)  $( 2 , - 5 )$ 
D)  $( - 2,5 )$

Question 7

Find the domain and range of the function.
-$$f ( x ) = - 10 x ^ { 2 } - 180 x - 816$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 9 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 6 ]$ 
C)  Domain: $( - \infty , - 6 ]$; Range: $[ 9 , \infty )$ 
D)  Domain: $( - \infty , - 6 ]$; Range: $[ 0 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 9 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 6 ]$ 
C)  Domain: $( - \infty , - 6 ]$; Range: $[ 9 , \infty )$ 
D)  Domain: $( - \infty , - 6 ]$; Range: $[ 0 , \infty )$

Question 8

Find the domain and range of the function.
-$$f ( x ) = - 3 - x ^ { 2 }$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 3 ]$ 
C)  Domain: $( - \infty , - 3 ]$; Range: $[ 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ - 3 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 3 ]$ 
C)  Domain: $( - \infty , - 3 ]$; Range: $[ 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ - 3 , \infty )$

Question 9

Provide an appropriate response.
-Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$-intercepts $- 9$ and $- 2$ and $\mathrm { y }$-intercept 6

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$ 
B)  $f ( x ) = x ^ { 2 } + 5 x + 6$ 
C)  $f ( x ) = x ^ { 2 } + 11 x + 18$ 
D)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$ 
A)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$ 
B)  $f ( x ) = x ^ { 2 } + 5 x + 6$ 
C)  $f ( x ) = x ^ { 2 } + 11 x + 18$ 
D)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$

Question 10

Find the equation that the given graph represents.
-$$f ( x ) = ( x - 2 ) ^ { 4 }$$

Accepted Answer

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

Question 11

Round your answer to two decimal places.
-$\mathrm { x }$ varies inversely as $\mathrm { v }$, and $\mathrm { x } = 42$ when $\mathrm { v } = 9$. Find $\mathrm { x }$ when $\mathrm { v } = 54$.

Accepted Answer

A)  7 
B)  63 
C)  6 
D)  81 
A)  7 
B)  63 
C)  6 
D)  81

Question 12

Provide an appropriate response.
-How many positive real zeros does this graph have?

Accepted Answer

A)  3 
B)  4 
C)  2 
D)  1 
A)  3 
B)  4 
C)  2 
D)  1

Question 13

Translate the given formula to an English phrase using the word "varies".
-$$\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h} \text {, where } \mathrm { V } \text { is the volume of a cylinder of radius } \mathrm { r } \text { and height } \mathrm { h } \text {. }$$

Accepted Answer

The volume of a cyli

Question 14

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=-2 x^{2}(x+2)(x+1)$

Accepted Answer

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

Question 15

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
-$$f ( x ) = - 4 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 9 x - 6$$

Accepted Answer

A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 2 & 0 \
2 & 0 & 2 \
0 & 4 & 0 \
0 & 2 & 2 \
0 & 0 & 4
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 0 \
2 & 2 & 0 \
2 & 0 & 2 \
0 & 4 & 0 \
0 & 2 & 2 \
0 & 0 & 4
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 2 & 0 \
2 & 0 & 2 \
0 & 2 & 2 \
0 & 0 & 2
\end{array}$ 
D) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 0 \
2 & 0 & 2 \
0 & 0 & 4
\end{array}$ 
A) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 2 & 0 \
2 & 0 & 2 \
0 & 4 & 0 \
0 & 2 & 2 \
0 & 0 & 4
\end{array}$ 
B) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 0 \
2 & 2 & 0 \
2 & 0 & 2 \
0 & 4 & 0 \
0 & 2 & 2 \
0 & 0 & 4
\end{array}$ 
C) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 2 & 2 & 0 \
2 & 0 & 2 \
0 & 2 & 2 \
0 & 0 & 2
\end{array}$ 
D) 
$\begin{array}{c|c|c}
\text { Positive } & \text { Negative } & \text { Nonreal Complex } \
\hline 4 & 0 & 0 \
2 & 0 & 2 \
0 & 0 & 4
\end{array}$

Question 16

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$$

Accepted Answer

A) True 
 B)False

Question 17

Find an equation for the rational function graph.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 262,500 } { x + 525 }$. What is the cost per ton for $x = 300 ?$

Accepted Answer

A)  $\$ 150,000.00$ 
B)  $\$ 318.18$ 
C)  $\$ 95,454.55$ 
D)  $\$ 350.00$ 
A)  $\$ 150,000.00$ 
B)  $\$ 318.18$ 
C)  $\$ 95,454.55$ 
D)  $\$ 350.00$

Question 18

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$5 + 4 i$ and $5 - 4 i$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } - 10 x + 9$ 
B)  $f ( x ) = x ^ { 2 } + 41$ 
C)  $f ( x ) = x ^ { 2 } + 10 x + 41$ 
D)  $f ( x ) = x ^ { 2 } - 10 x + 41$ 
A)  $f ( x ) = x ^ { 2 } - 10 x + 9$ 
B)  $f ( x ) = x ^ { 2 } + 41$ 
C)  $f ( x ) = x ^ { 2 } + 10 x + 41$ 
D)  $f ( x ) = x ^ { 2 } - 10 x + 41$

Question 19

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for
the given value of k.
-$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; k = 2$$

Accepted Answer

A)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } - 7 x + 11 \right) + 18$ 
B)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + 7 x + 9 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + x - 3 \right) - 2$ 
D)  $f ( x ) = ( x + 2 ) \left( 2 x ^ { 2 } + x + 3 \right) + 10$ 
A)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } - 7 x + 11 \right) + 18$ 
B)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + 7 x + 9 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + x - 3 \right) - 2$ 
D)  $f ( x ) = ( x + 2 ) \left( 2 x ^ { 2 } + x + 3 \right) + 10$

Question 20

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = 0$; horizontal: $y = - 4 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
B)  Vertical: $x = - 4$; horizontal: $y = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = - 4$; horizontal: $y = 0 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
D)  Vertical: $x = 0$; horizontal: $y = - 4 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Vertical: $x = 0$; horizontal: $y = - 4 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
B)  Vertical: $x = - 4$; horizontal: $y = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = - 4$; horizontal: $y = 0 ; ( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
D)  Vertical: $x = 0$; horizontal: $y = - 4 ; ( - \infty , 0 ) \cup ( 0 , \infty )$

Use the remainder theorem and synthetic division to find f(k). - $k = 5 ; f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 2$

Use the remainder theorem and synthetic division to find f(k). - $k = 4 ; f ( x ) = 4 x ^ { 4 } + 3 x ^ { 3 } + 3 x ^ { 2 } - 6 x + 22$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

Identify the vertex of the parabola. - $y = 3 x ^ { 2 } + 12 x + 17$

Find the domain and range of the function. - $f ( x ) = - 10 x ^ { 2 } - 180 x - 816$

Find the domain and range of the function. - $f ( x ) = - 3 - x ^ { 2 }$

Provide an appropriate response. -Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$ -intercepts $- 9$ and $- 2$ and $\mathrm { y }$ -intercept 6

Find the equation that the given graph represents. - $f ( x ) = ( x - 2 ) ^ { 4 }$ $Find the equation that the given graph represents. - f ( x ) = ( x - 2 ) ^ { 4 }$

Round your answer to two decimal places. - $\mathrm { x }$ varies inversely as $\mathrm { v }$ , and $\mathrm { x } = 42$ when $\mathrm { v } = 9$ . Find $\mathrm { x }$ when $\mathrm { v } = 54$ .

Provide an appropriate response. -How many positive real zeros does this graph have?

Translate the given formula to an English phrase using the word "varies". - $\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h} \text {, where } \mathrm { V } \text { is the volume of a cylinder of radius } \mathrm { r } \text { and height } \mathrm { h } \text {. }$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-2 x^{2}(x+2)(x+1)$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=-2 x^{2}(x+2)(x+1)$

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. - $f ( x ) = - 4 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } + 9 x - 6$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x ^ { 2 } } { x ^ { 2 } + 5 } \text { has a horizontal asymptote of } y = - 1 \text {. }$

Find an equation for the rational function graph. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 262,500 } { x + 525 }$ . What is the cost per ton for $x = 300 ?$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $5 + 4 i$ and $5 - 4 i$

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; k = 2$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions

Use the remainder theorem and synthetic division to find f(k). - k=5;f(x)=x3−3x2−4x+2k = 5 ; f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x + 2k=5;f(x)=x3−3x2−4x+2

Use the remainder theorem and synthetic division to find f(k). - k=4;f(x)=4x4+3x3+3x2−6x+22k = 4 ; f ( x ) = 4 x ^ { 4 } + 3 x ^ { 3 } + 3 x ^ { 2 } - 6 x + 22k=4;f(x)=4x4+3x3+3x2−6x+22

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=3x2+8x+cf ( x ) = 3 x ^ { 2 } + 8 x + cf(x)=3x2+8x+c have exactly one xxx -intercept?

Identify the vertex of the parabola. - y=3x2+12x+17y = 3 x ^ { 2 } + 12 x + 17y=3x2+12x+17

Find the domain and range of the function. - f(x)=−10x2−180x−816f ( x ) = - 10 x ^ { 2 } - 180 x - 816f(x)=−10x2−180x−816

Find the domain and range of the function. - f(x)=−3−x2f ( x ) = - 3 - x ^ { 2 }f(x)=−3−x2

Provide an appropriate response. -Find a quadratic function f\mathrm { f }f having x\mathrm { x }x -intercepts −9- 9−9 and −2- 2−2 and y\mathrm { y }y -intercept 6

Find the equation that the given graph represents. - f(x)=(x−2)4f ( x ) = ( x - 2 ) ^ { 4 }f(x)=(x−2)4

Round your answer to two decimal places. - x\mathrm { x }x varies inversely as v\mathrm { v }v , and x=42\mathrm { x } = 42x=42 when v=9\mathrm { v } = 9v=9 . Find x\mathrm { x }x when v=54\mathrm { v } = 54v=54 .