Question 1

Sketch the graph of the parabola.
-$y=(x-5)^{2}+2$

Accepted Answer

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

Question 2

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

Accepted Answer

A)  Domain: $( 2 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ - 2 , \infty )$ 
C)  Domain: $( - \infty , - 2 )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 )$ 
A)  Domain: $( 2 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ - 2 , \infty )$ 
C)  Domain: $( - \infty , - 2 )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 )$

Question 3

Find the domain and range of the function.
-$$f ( x ) = ( x + 1 ) ^ { 2 } + 5$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $( - 5 , \infty )$ 
B)  Domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( 5 , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$ 
A)  Domain: $( - \infty , \infty )$; range: $( - 5 , \infty )$ 
B)  Domain: $( - 5 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( 5 , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$

Question 4

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } } , \text { where } \mathrm { P } \text { is the gas pressure of } \mathrm { N } \text { molecules of a gas in a volume } \mathrm { V } \text { at }$$

Accepted Answer

Pressure varies dire

Question 5

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

Accepted Answer

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

Question 6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$3 - 2 i ; f ( x ) = x ^ { 2 } + 6 x + 13$

Accepted Answer

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

Question 7

Graph the function.
-$f(x)=\frac{10}{x^{2}}-1$

Accepted Answer

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

Question 8

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$$

Accepted Answer

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

Question 9

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$$3 x ^ { 2 } - 4 x + 20 ; x - 2$$

Accepted Answer

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

Question 10

Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }$$

Accepted Answer

A)  $x ^ { 2 } + 3 x + 4$ 
B)  $x ^ { 2 } + 3 x + 2$ 
C)  $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 2 } { x + 1 }$ 
D)  $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 14 } { 9 } + \frac { 16 } { 27 }$ 
A)  $x ^ { 2 } + 3 x + 4$ 
B)  $x ^ { 2 } + 3 x + 2$ 
C)  $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 2 } { x + 1 }$ 
D)  $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 14 } { 9 } + \frac { 16 } { 27 }$

Question 11

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = - 2 x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 6 x + 8$$

Accepted Answer

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

Question 12

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$$

Accepted Answer

A)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$; Range: $( - \infty , 5 )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 5 , \infty )$ 
A)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$; Range: $( - \infty , 5 )$ 
C)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty )$; Range: $( 5 , \infty )$

Question 13

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$-intercepts?

Accepted Answer

A)  $a  \frac { 16 } { 5 }$ 
C)  $\mathrm { a }  \frac { 4 } { 5 }$ 
A)  $a  \frac { 16 } { 5 }$ 
C)  $\mathrm { a }  \frac { 4 } { 5 }$

Question 14

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$$- 8 x ^ { 3 } + 22 x ^ { 2 } - 5 x + 3 ; x + 3$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 15

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

Accepted Answer

A)  Horizontal: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Horizontal: $x = 0 ; ( - \infty , \infty )$ 
C)  Horizontal: $y = 0 ; ( - \infty , \infty )$ 
D)  Vertical: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Horizontal: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Horizontal: $x = 0 ; ( - \infty , \infty )$ 
C)  Horizontal: $y = 0 ; ( - \infty , \infty )$ 
D)  Vertical: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$

Question 16

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=(3 x+2)(x+1)^{2}$

Accepted Answer

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

Question 17

Solve the problem.
-y varies directly as the square of z and y = 448 when z = 8. Find y when z is 5.

Accepted Answer

A)  56 
B)  40 
C)  175 
D)  280 
A)  56 
B)  40 
C)  175 
D)  280

Question 18

Solve the problem.
-The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 36 hours for 7 carpenters to frame a house, then how long will it take 54 carpenters
To do the same job?

Accepted Answer

A)  40 hr 
B)  10.5 hr 
C)  4.7 hr 
D)  54 hr 
A)  40 hr 
B)  10.5 hr 
C)  4.7 hr 
D)  54 hr

Question 19

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { ( x - 4 ) ( x - 8 ) } { ( x + 2 ) ( x - 8 ) }$ 
B)  $f ( x ) = \frac { ( x + 2 ) ( x - 8 ) } { ( x - 4 ) ( x - 8 ) }$ 
C)  $f ( x ) = \frac { x + 2 } { x - 4 }$ 
D)  $f ( x ) = \frac { ( x - 2 ) ( x + 8 ) } { ( x + 4 ) ( x + 8 ) }$ 
A)  $f ( x ) = \frac { ( x - 4 ) ( x - 8 ) } { ( x + 2 ) ( x - 8 ) }$ 
B)  $f ( x ) = \frac { ( x + 2 ) ( x - 8 ) } { ( x - 4 ) ( x - 8 ) }$ 
C)  $f ( x ) = \frac { x + 2 } { x - 4 }$ 
D)  $f ( x ) = \frac { ( x - 2 ) ( x + 8 ) } { ( x + 4 ) ( x + 8 ) }$

Question 20

Find the zeros of the polynomial function and state the multiplicity of each.
-$5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 3 }$

Accepted Answer

A)  0 (multiplicity $1 ), - 6$ (multiplicity $1 ), \pm 4$ (multiplicity 1 ) 
B)  0 (multiplicity 1), $- 6$ (multiplicity 1 ), $- 16$ (multiplicity 3 ) 
C)  0 (multiplicity 1), 6 (multiplicity 1), $\pm 4$ (multiplicity 3) 
D)  0 (multiplicity 1 ), $- 6$ (multiplicity $1 ), \pm 4$ (multiplicity 3 ) 
A)  0 (multiplicity $1 ), - 6$ (multiplicity $1 ), \pm 4$ (multiplicity 1 ) 
B)  0 (multiplicity 1), $- 6$ (multiplicity 1 ), $- 16$ (multiplicity 3 ) 
C)  0 (multiplicity 1), 6 (multiplicity 1), $\pm 4$ (multiplicity 3) 
D)  0 (multiplicity 1 ), $- 6$ (multiplicity $1 ), \pm 4$ (multiplicity 3 )

Sketch the graph of the parabola. - $y=(x-5)^{2}+2$ $Sketch the graph of the parabola. - y=(x-5)^{2}+2$

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

Find the domain and range of the function. - $f ( x ) = ( x + 1 ) ^ { 2 } + 5$

Translate the given formula to an English phrase using the word ʺvariesʺ. - $\mathrm { P } = \frac { \mathrm { kNT } } { \mathrm { V } } , \text { where } \mathrm { P } \text { is the gas pressure of } \mathrm { N } \text { molecules of a gas in a volume } \mathrm { V } \text { at }$

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

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $3 - 2 i ; f ( x ) = x ^ { 2 } + 6 x + 13$

Graph the function. - $f(x)=\frac{10}{x^{2}}-1$ $Graph the function. - f(x)=\frac{10}{x^{2}}-1$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $3 x ^ { 2 } - 4 x + 20 ; x - 2$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 6 x + 8$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 8 x ^ { 3 } + 22 x ^ { 2 } - 5 x + 3 ; x + 3$

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

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(3 x+2)(x+1)^{2}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=(3 x+2)(x+1)^{2}$

Solve the problem. -y varies directly as the square of z and y = 448 when z = 8. Find y when z is 5.

Solve the problem. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 36 hours for 7 carpenters to frame a house, then how long will it take 54 carpenters To do the same job?

Find an equation for the rational function graph. -

Find the zeros of the polynomial function and state the multiplicity of each. - $5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 3 }$

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

Sketch the graph of the parabola. - y=(x−5)2+2y=(x-5)^{2}+2y=(x−5)2+2

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

Find the domain and range of the function. - f(x)=(x+1)2+5f ( x ) = ( x + 1 ) ^ { 2 } + 5f(x)=(x+1)2+5

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

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - 3−2i;f(x)=x2+6x+133 - 2 i ; f ( x ) = x ^ { 2 } + 6 x + 133−2i;f(x)=x2+6x+13

Graph the function. - f(x)=10x2−1f(x)=\frac{10}{x^{2}}-1f(x)=x210​−1

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=2x3−3x2−5x+4;k=2f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2f(x)=2x3−3x2−5x+4;k=2

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 3x2−4x+20;x−23 x ^ { 2 } - 4 x + 20 ; x - 23x2−4x+20;x−2

Use synthetic division to perform the division. - x3+83x2+1x−23x−13\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }x−31​x3+38​x2+1x−32​​

Find the correct end behavior diagram for the given polynomial function. - P(x)=−2x6+8x5−x2−6x+8P ( x ) = - 2 x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 6 x + 8P(x)=−2x6+8x5−x2−6x+8

Give the domain and range for the rational function. Use interval notation. - f(x)=1(x−3)2+5f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5f(x)=(x−3)21​+5

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5 have two xxx -intercepts?

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - −8x3+22x2−5x+3;x+3- 8 x ^ { 3 } + 22 x ^ { 2 } - 5 x + 3 ; x + 3−8x3+22x2−5x+3;x+3

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

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=(3x+2)(x+1)2f(x)=(3 x+2)(x+1)^{2}f(x)=(3x+2)(x+1)2

Solve the problem. -y varies directly as the square of z and y = 448 when z = 8. Find y when z is 5.

Solve the problem. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 36 hours for 7 carpenters to frame a house, then how long will it take 54 carpenters To do the same job?

Find an equation for the rational function graph. -

Find the zeros of the polynomial function and state the multiplicity of each. - 5x(x+6)(x2−16)35 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 3 }5x(x+6)(x2−16)3

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. - $y=(x-5)^{2}+2$ $Sketch the graph of the parabola. - y=(x-5)^{2}+2$

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

Find the domain and range of the function. - $f ( x ) = ( x + 1 ) ^ { 2 } + 5$

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

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $3 - 2 i ; f ( x ) = x ^ { 2 } + 6 x + 13$

Graph the function. - $f(x)=\frac{10}{x^{2}}-1$ $Graph the function. - f(x)=\frac{10}{x^{2}}-1$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $3 x ^ { 2 } - 4 x + 20 ; x - 2$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 6 x + 8$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { ( x - 3 ) ^ { 2 } } + 5$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $- 8 x ^ { 3 } + 22 x ^ { 2 } - 5 x + 3 ; x + 3$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(3 x+2)(x+1)^{2}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=(3 x+2)(x+1)^{2}$

Find the zeros of the polynomial function and state the multiplicity of each. - $5 x ( x + 6 ) \left( x ^ { 2 } - 16 \right) ^ { 3 }$