Question 1

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Accepted Answer

A) True 
 B)False

Question 2

Provide an appropriate response.
-Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 2 } { x - 9 }$

Accepted Answer

A)  Approaches $\infty$ from the left and the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
D)  Approaches $- \infty$ from the left and the right 
A)  Approaches $\infty$ from the left and the right 
B)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
C)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
D)  Approaches $- \infty$ from the left and the right

Question 3

Solve the inequality. Write the solution set in interval notation.
-$$3 x ^ { 2 } - 8 x \geq 16$$

Accepted Answer

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

Question 4

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 3 x ^ { 3 } + 32 x ^ { 2 } + 32 x + 27$$

Accepted Answer

A)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$ 
B)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
D)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$ 
A)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$ 
B)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
D)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$

Question 5

Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

Accepted Answer

A)  $1 , - 1 , - 8 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 8 )$ 
B)  $1 , - 2,10 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x - 10 )$ 
C)  $1 , - 1,8 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 8 )$ 
D)  $1 , - 1 , - 9 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 9 )$ 
A)  $1 , - 1 , - 8 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 8 )$ 
B)  $1 , - 2,10 ; f ( x ) = ( x - 1 ) ( x + 2 ) ( x - 10 )$ 
C)  $1 , - 1,8 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 8 )$ 
D)  $1 , - 1 , - 9 ; f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 9 )$

Question 6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = 5 i ; f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$

Accepted Answer

A) True 
 B)False

Question 7

If y varies directly as the square of x, and x is doubled, how is y changed?

Accepted Answer

A)  y is half as large as before 
B)  y is one-quarter as large as before 
C)  y is twice as large as before 
D)  y is four times as large as before 
A)  y is half as large as before 
B)  y is one-quarter as large as before 
C)  y is twice as large as before 
D)  y is four times as large as before

Question 8

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

Accepted Answer

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

Question 9

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = - \frac { 1 } { ( x - 8 ) ^ { 2 } } + 9$$

Accepted Answer

A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 9 )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 9 )$ 
C)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( 9 , \infty )$ 
D)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 )$ 
A)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 9 )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 9 )$ 
C)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( 9 , \infty )$ 
D)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 )$

Question 10

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

Accepted Answer

A)  Vertical: $x = - 3$; horizontal: $y = 0 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  Vertical: $x = 0$; horizontal: $y = - 3 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = 0$; horizontal: $y = - 3 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  Vertical: $\mathrm { x } = - 3$; horizontal: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Vertical: $x = - 3$; horizontal: $y = 0 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  Vertical: $x = 0$; horizontal: $y = - 3 ; ( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Vertical: $x = 0$; horizontal: $y = - 3 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  Vertical: $\mathrm { x } = - 3$; horizontal: $\mathrm { y } = 0 ; ( - \infty , 0 ) \cup ( 0 , \infty )$

Question 11

Translate the given formula to an English phrase using the word "varies".
-$\mathrm { A } = \pi \mathrm { r } ^ { 2 }$ , where A is the area of a circle of radius r.

Accepted Answer

The area of a circle

Question 12

Determine whether the statement is true or false.
-$$\text { If } c \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d }$$

Accepted Answer

A) True 
 B)False

Question 13

What type of variation is suggested by the graph?

Accepted Answer

A)  y varies inversely as the square of x 
B)  y varies directly as x 
C)  y varies inversely as x 
D)  y varies directly as the square of x 
A)  y varies inversely as the square of x 
B)  y varies directly as x 
C)  y varies inversely as x 
D)  y varies directly as the square of x

Question 14

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 6 x ^ { 3 } + 7 x ^ { 2 } - 2 x + 9$$

Accepted Answer

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

Question 15

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-

Accepted Answer

A)  linear; positive 
B)  linear; negative 
C)  quadratic; negative 
D)  quadratic; positive 
A)  linear; positive 
B)  linear; negative 
C)  quadratic; negative 
D)  quadratic; positive

Question 16

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Accepted Answer

A) True 
 B)False

Question 17

Give the equations of any horizontal asymptotes.
-$$f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$$

Accepted Answer

A)  none 
B)  $y = 1$ 
C)  $\mathrm { y } = 8$ 
D)  $y = - 8$ 
A)  none 
B)  $y = 1$ 
C)  $\mathrm { y } = 8$ 
D)  $y = - 8$

Question 18

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

Accepted Answer

A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 1 ) \cup ( 1 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
A)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , - 1 ) \cup ( - 1 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  Domain: $( - \infty , 1 ) \cup ( 1 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 1 ) \cup ( - 1 , \infty )$

Question 19

Give the equations of any vertical asymptotes.
-$$f ( x ) = \frac { 3 x + 5 } { 5 x - 2 }$$

Accepted Answer

A)  $x = \frac { 2 } { 5 }$ 
B)  $x = \frac { 3 } { 5 }$ 
C)  $x = - \frac { 5 } { 2 }$ 
D)  $x = \frac { 5 } { 2 }$ 
A)  $x = \frac { 2 } { 5 }$ 
B)  $x = \frac { 3 } { 5 }$ 
C)  $x = - \frac { 5 } { 2 }$ 
D)  $x = \frac { 5 } { 2 }$

Question 20

Round to the nearest tenth unless indicated otherwise.
-At a fixed temperature, the resistance R of a wire varies directly as the length l and inversely as the square of its diameter d. If the resistance is 0.46 ohm when the diameter is 1 mm and the length is 230 cm, what is the
Resistance when the diameter is 2 mm and the length is 2170 cm?

Accepted Answer

A)  1.1 ohm 
B)  542.5 ohm 
C)  249.6 ohm 
D)  2.2 ohm 
A)  1.1 ohm 
B)  542.5 ohm 
C)  249.6 ohm 
D)  2.2 ohm

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 2 } { x - 9 }$

Solve the inequality. Write the solution set in interval notation. - $3 x ^ { 2 } - 8 x \geq 16$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 3 x ^ { 3 } + 32 x ^ { 2 } + 32 x + 27$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 5 i ; f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$

If y varies directly as the square of x, and x is doubled, how is y changed?

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

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 8 ) ^ { 2 } } + 9$

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

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \pi \mathrm { r } ^ { 2 }$ , where A is the area of a circle of radius r.

Determine whether the statement is true or false. - $\text { If } c \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d }$

What type of variation is suggested by the graph?

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 6 x ^ { 3 } + 7 x ^ { 2 } - 2 x + 9$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Give the equations of any horizontal asymptotes. - $f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$

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

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { 3 x + 5 } { 5 x - 2 }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 6x4+13x3−2x2+x+4;x+26 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 26x4+13x3−2x2+x+4;x+2

Provide an appropriate response. -Explain the behavior of the graph of f(x)f ( x )f(x) as it approaches its vertical asymptote. f(x)=−2x−9f ( x ) = \frac { - 2 } { x - 9 }f(x)=x−9−2​

Solve the inequality. Write the solution set in interval notation. - 3x2−8x≥163 x ^ { 2 } - 8 x \geq 163x2−8x≥16

Give all possible rational zeros for the following polynomial. - P(x)=3x3+32x2+32x+27P ( x ) = 3 x ^ { 3 } + 32 x ^ { 2 } + 32 x + 27P(x)=3x3+32x2+32x+27

Find all rational zeros and factor f(x). - f(x)=x3+8x2−x−8f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8f(x)=x3+8x2−x−8

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=5i;f(x)=x3+5x2+25x+125k = 5 i ; f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125k=5i;f(x)=x3+5x2+25x+125

If y varies directly as the square of x, and x is doubled, how is y changed?

Sketch the graph of the parabola. - f(x)=(x+1)2f(x)=(x+1)^{2}f(x)=(x+1)2

Give the domain and range for the rational function. Use interval notation. - f(x)=−1(x−8)2+9f ( x ) = - \frac { 1 } { ( x - 8 ) ^ { 2 } } + 9f(x)=−(x−8)21​+9

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

Translate the given formula to an English phrase using the word "varies". - A=πr2\mathrm { A } = \pi \mathrm { r } ^ { 2 }A=πr2 , where A is the area of a circle of radius r.

Determine whether the statement is true or false. - If c and d are complex numbers, then c−d‾=cˉ−dˉ\text { If } c \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d } If c and d are complex numbers, then c−d​=cˉ−dˉ

What type of variation is suggested by the graph?

Find the correct end behavior diagram for the given polynomial function. - P(x)=6x3+7x2−2x+9P ( x ) = 6 x ^ { 3 } + 7 x ^ { 2 } - 2 x + 9P(x)=6x3+7x2−2x+9

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x2x ^ { 2 }x2 should be positive or negative. -

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 6x4+11x3−2x2+x+4;x+26 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 26x4+11x3−2x2+x+4;x+2

Give the equations of any horizontal asymptotes. - f(x)=4x2+84x2−8f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }f(x)=4x2−84x2+8​

Give the domain and range for the rational function. Use interval notation. - f(x)=1x+1f ( x ) = \frac { 1 } { x + 1 }f(x)=x+11​

Give the equations of any vertical asymptotes. - f(x)=3x+55x−2f ( x ) = \frac { 3 x + 5 } { 5 x - 2 }f(x)=5x−23x+5​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Provide an appropriate response. -Explain the behavior of the graph of $f ( x )$ as it approaches its vertical asymptote. $f ( x ) = \frac { - 2 } { x - 9 }$

Solve the inequality. Write the solution set in interval notation. - $3 x ^ { 2 } - 8 x \geq 16$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 3 x ^ { 3 } + 32 x ^ { 2 } + 32 x + 27$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 5 i ; f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 25 x + 125$

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

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 8 ) ^ { 2 } } + 9$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \pi \mathrm { r } ^ { 2 }$ , where A is the area of a circle of radius r.

Determine whether the statement is true or false. - $\text { If } c \text { and } d \text { are complex numbers, then } \overline { c - d } = \bar { c } - \bar { d }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 6 x ^ { 3 } + 7 x ^ { 2 } - 2 x + 9$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Give the equations of any horizontal asymptotes. - $f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$

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

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { 3 x + 5 } { 5 x - 2 }$