Question 1

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
B)  $P ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
C)  $P ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$ 
D)  $P ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$ 
A)  $P ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
B)  $P ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
C)  $P ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$ 
D)  $P ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$

Question 2

Sketch the graph of the parabola.
-$y=4(x-1)^{2}+3$

Accepted Answer

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

Question 3

Solve the problem.
-In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : f ( x ) = \frac { 0.47 x } { 100.5 - x }$. How many hours of study are needed to score 83 ?

Accepted Answer

A)  $22.30 \mathrm { hr }$ 
B)  $2.23 \mathrm { hr }$ 
C)  $100.93 \mathrm { hr }$ 
D)  $4.51 \mathrm { hr }$ 
A)  $22.30 \mathrm { hr }$ 
B)  $2.23 \mathrm { hr }$ 
C)  $100.93 \mathrm { hr }$ 
D)  $4.51 \mathrm { hr }$

Question 4

Sketch the graph of the parabola.
-$y=4 x^{2}+3 x-8$

Accepted Answer

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

Question 5

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$$

Accepted Answer

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

Question 6

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = 2 x ^ { 4 } - x ^ { 2 } + 4$ 
B)  $P ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 3 x + 4$ 
C)  $P ( x ) = - x ^ { 3 } - x - 4$ 
D)  $P ( x ) = - x ^ { 4 } + x ^ { 2 } - 3 x - 4$ 
A)  $P ( x ) = 2 x ^ { 4 } - x ^ { 2 } + 4$ 
B)  $P ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 3 x + 4$ 
C)  $P ( x ) = - x ^ { 3 } - x - 4$ 
D)  $P ( x ) = - x ^ { 4 } + x ^ { 2 } - 3 x - 4$

Question 7

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - 3 x ^ { 5 } + x ^ { 4 } + 2 x$ 
B)  $P ( x ) = 2 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
C)  $P ( x ) = 2 x ^ { 5 } + x ^ { 3 } + 8 x ^ { 2 } - 4 x + 3$ 
D)  $P ( x ) = - x ^ { 4 } + x ^ { 3 } - x$ 
A)  $P ( x ) = - 3 x ^ { 5 } + x ^ { 4 } + 2 x$ 
B)  $P ( x ) = 2 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
C)  $P ( x ) = 2 x ^ { 5 } + x ^ { 3 } + 8 x ^ { 2 } - 4 x + 3$ 
D)  $P ( x ) = - x ^ { 4 } + x ^ { 3 } - x$

Question 8

Determine whether the statement is true or false.
-If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.

Accepted Answer

A) True 
 B)False

Question 9

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$\mathrm { C } = 2 \pi \mathrm { r } \text {, where } \mathrm { C } \text { is the circumference of a circle of radius }$$

Accepted Answer

The circumference of

Question 10

Determine whether the statement is true or false.
-$$\text { If } c \text { is a complex number, then } 5 \bar { c } = \overline { 5 c }$$

Accepted Answer

A) True 
 B)False

Question 11

Give the equatiosn of any horizontal asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 2 } { x ^ { 2 } - 2 }$$

Accepted Answer

A)  $y = 0$ 
B)  none 
C)  $y = 1$ 
D)  $y = 2$ 
A)  $y = 0$ 
B)  none 
C)  $y = 1$ 
D)  $y = 2$

Question 12

Use synthetic division to perform the division.
-$$\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$$

Accepted Answer

A)  $- 6 x ^ { 2 } - 10 x - 5 + \frac { - 10 } { x - 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x - 2 }$ 
C)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 25 } { x - 2 }$ 
D)  $- 6 x ^ { 2 } - 10 x - 25 + \frac { - 40 } { x - 2 }$ 
A)  $- 6 x ^ { 2 } - 10 x - 5 + \frac { - 10 } { x - 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x - 2 }$ 
C)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 25 } { x - 2 }$ 
D)  $- 6 x ^ { 2 } - 10 x - 25 + \frac { - 40 } { x - 2 }$

Question 13

Solve the problem.
-If $f$ varies jointly as $q ^ { 2 }$ and $h$, and $f = 36$ when $q = 2$ and $h = 3$, find $q$ when $f = 288$ and $h = 6$.

Accepted Answer

A)  3 
B)  2 
C)  6 
D)  4 
A)  3 
B)  2 
C)  6 
D)  4

Question 14

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-5)^{2}-2$
 
Find the coordinates of the vertex.

Accepted Answer

A)  $( 5,0 )$ 
B)  $( - 5 , - 2 )$ 
C)  $( - 5,2 )$ 
D)  $( 5 , - 2 )$ 
A)  $( 5,0 )$ 
B)  $( - 5 , - 2 )$ 
C)  $( - 5,2 )$ 
D)  $( 5 , - 2 )$

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 7$ and $x = - 2$, horizontal asymptote $y = 7$

Accepted Answer

To find an equation for a rational funct

Question 16

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4$$

Accepted Answer

A)  $1 + 2 i , 1 - 2 i$ 
B)  $- 1 + 2 i , - 1 - 2 i$ 
C)  $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
D)  $1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$ 
A)  $1 + 2 i , 1 - 2 i$ 
B)  $- 1 + 2 i , - 1 - 2 i$ 
C)  $1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
D)  $1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$

Question 17

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $- 5$ and 4 , y-intercept: 2, vertical asymptotes: $x = - 2$ and $x = 5$, horizontal asymptote: $y = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x + 5 ) ( x - 4 ) } { ( x + 2 ) ( x - 5 ) }$ 
B)  $f ( x ) = \frac { ( x + 2 ) ( x - 5 ) } { ( x + 5 ) ( x - 4 ) }$ 
C)  $f ( x ) = \frac { ( x - 2 ) ( x + 5 ) } { ( x - 5 ) ( x + 4 ) }$ 
D)  $f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { ( x - 2 ) ( x + 5 ) }$ 
A)  $f ( x ) = \frac { ( x + 5 ) ( x - 4 ) } { ( x + 2 ) ( x - 5 ) }$ 
B)  $f ( x ) = \frac { ( x + 2 ) ( x - 5 ) } { ( x + 5 ) ( x - 4 ) }$ 
C)  $f ( x ) = \frac { ( x - 2 ) ( x + 5 ) } { ( x - 5 ) ( x + 4 ) }$ 
D)  $f ( x ) = \frac { ( x - 5 ) ( x + 4 ) } { ( x - 2 ) ( x + 5 ) }$

Question 18

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 24$

Accepted Answer

A)  $P ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } - 6 x$ 
B)  $P ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
C)  $P ( x ) = 3 x ^ { 3 } + 9 x ^ { 2 } - 6 x$ 
D)  $P ( x ) = 3 x ^ { 2 } + 3 x - 6$ 
A)  $P ( x ) = 3 x ^ { 3 } + 3 x ^ { 2 } - 6 x$ 
B)  $P ( x ) = 3 x ^ { 3 } - 3 x ^ { 2 } - 6 x$ 
C)  $P ( x ) = 3 x ^ { 3 } + 9 x ^ { 2 } - 6 x$ 
D)  $P ( x ) = 3 x ^ { 2 } + 3 x - 6$

Question 19

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 4 - 8 x + x ^ { 2 } - x ^ { 3 } - 8 x ^ { 4 }$$

Accepted Answer

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

Question 20

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-1)^{2}-5$

Find the $y$-intercept.

Accepted Answer

A)  $( 4,0 )$ 
B)  $( 0 , - 4 )$ 
C)  $( 0 , - 3 )$ 
D)  $( - 4,0 )$ 
A)  $( 4,0 )$ 
B)  $( 0 , - 4 )$ 
C)  $( 0 , - 3 )$ 
D)  $( - 4,0 )$

Find the equation that the given graph represents. -

Sketch the graph of the parabola. - $y=4(x-1)^{2}+3$ $Sketch the graph of the parabola. - y=4(x-1)^{2}+3$

Solve the problem. -In the following formula, $\mathrm { f } ( \mathrm { x } )$ is the minimum number of hours of studying required to attain a test score of $x : f ( x ) = \frac { 0.47 x } { 100.5 - x }$ . How many hours of study are needed to score 83 ?

Sketch the graph of the parabola. - $y=4 x^{2}+3 x-8$ $Sketch the graph of the parabola. - y=4 x^{2}+3 x-8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$

Find the equation that the given graph represents. -

Find the equation that the given graph represents. -

Determine whether the statement is true or false. -If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { C } = 2 \pi \mathrm { r } \text {, where } \mathrm { C } \text { is the circumference of a circle of radius }$

Determine whether the statement is true or false. - $\text { If } c \text { is a complex number, then } 5 \bar { c } = \overline { 5 c }$

Give the equatiosn of any horizontal asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 2 } { x ^ { 2 } - 2 }$

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Solve the problem. -If $f$ varies jointly as $q ^ { 2 }$ and $h$ , and $f = 36$ when $q = 2$ and $h = 3$ , find $q$ when $f = 288$ and $h = 6$ .

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 7$ and $x = - 2$ , horizontal asymptote $y = 7$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $- 5$ and 4 , y-intercept: 2, vertical asymptotes: $x = - 2$ and $x = 5$ , horizontal asymptote: $y = 1$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 24$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 4 - 8 x + x ^ { 2 } - x ^ { 3 } - 8 x ^ { 4 }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-1)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-1)^{2}-5 Find the y -intercept.$ Find the $y$ -intercept.

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

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Find the equation that the given graph represents. -

Sketch the graph of the parabola. - y=4(x−1)2+3y=4(x-1)^{2}+3y=4(x−1)2+3

Sketch the graph of the parabola. - y=4x2+3x−8y=4 x^{2}+3 x-8y=4x2+3x−8

Sketch the graph of the rational function. - f(x)=x2+6x−7x2−x−20f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }f(x)=x2−x−20x2+6x−7​

Find the equation that the given graph represents. -

Find the equation that the given graph represents. -

Determine whether the statement is true or false. -If x - 3 is a factor of a polynomial f(x), then f(-3) = 0.

Determine whether the statement is true or false. - If c is a complex number, then 5cˉ=5c‾\text { If } c \text { is a complex number, then } 5 \bar { c } = \overline { 5 c } If c is a complex number, then 5cˉ=5c

Give the equatiosn of any horizontal asymptotes. - f(x)=x2+2x2−2f ( x ) = \frac { x ^ { 2 } + 2 } { x ^ { 2 } - 2 }f(x)=x2−2x2+2​

Use synthetic division to perform the division. - −6x3+2x2+5x−10x−2\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }x−2−6x3+2x2+5x−10​

Solve the problem. -If fff varies jointly as q2q ^ { 2 }q2 and hhh , and f=36f = 36f=36 when q=2q = 2q=2 and h=3h = 3h=3 , find qqq when f=288f = 288f=288 and h=6h = 6h=6 .

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−5)2−2f(x)=(x-5)^{2}-2f(x)=(x−5)2−2 Find the coordinates of the vertex.

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptotes x=7x = 7x=7 and x=−2x = - 2x=−2 , horizontal asymptote y=7y = 7y=7

For the polynomial, one zero is given. Find all others. - P(x)=x3−6x2+13x−20;4P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4P(x)=x3−6x2+13x−20;4

Determine which of the rational functions given below has the following feature(s). -x-intercepts: −5- 5−5 and 4 , y-intercept: 2, vertical asymptotes: x=−2x = - 2x=−2 and x=5x = 5x=5 , horizontal asymptote: y=1y = 1y=1

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −2,1,0- 2,1,0−2,1,0 and P(2)=24\mathrm { P } ( 2 ) = 24P(2)=24

Find the correct end behavior diagram for the given polynomial function. - P(x)=4−8x+x2−x3−8x4P ( x ) = 4 - 8 x + x ^ { 2 } - x ^ { 3 } - 8 x ^ { 4 }P(x)=4−8x+x2−x3−8x4

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−1)2−5f(x)=(x-1)^{2}-5f(x)=(x−1)2−5 Find the yyy -intercept.

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

Review of Basic Concepts

Filters

Sketch the graph of the parabola. - $y=4(x-1)^{2}+3$ $Sketch the graph of the parabola. - y=4(x-1)^{2}+3$

Sketch the graph of the parabola. - $y=4 x^{2}+3 x-8$ $Sketch the graph of the parabola. - y=4 x^{2}+3 x-8$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 20 }$

Determine whether the statement is true or false. - $\text { If } c \text { is a complex number, then } 5 \bar { c } = \overline { 5 c }$

Give the equatiosn of any horizontal asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 2 } { x ^ { 2 } - 2 }$

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

Solve the problem. -If $f$ varies jointly as $q ^ { 2 }$ and $h$ , and $f = 36$ when $q = 2$ and $h = 3$ , find $q$ when $f = 288$ and $h = 6$ .

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptotes $x = 7$ and $x = - 2$ , horizontal asymptote $y = 7$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; 4$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: $- 5$ and 4 , y-intercept: 2, vertical asymptotes: $x = - 2$ and $x = 5$ , horizontal asymptote: $y = 1$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 2,1,0$ and $\mathrm { P } ( 2 ) = 24$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 4 - 8 x + x ^ { 2 } - x ^ { 3 } - 8 x ^ { 4 }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-1)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-1)^{2}-5 Find the y -intercept.$ Find the $y$ -intercept.