Question 1

Find the domain of the rational function.
-$$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$$

Accepted Answer

A)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
B)  $\{ x \mid x \neq 3 , x \neq - 5 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3 , x \neq 5 \}$ 
A)  $\{ x \mid x \neq 3 , x \neq - 3 , x \neq - 5 \}$ 
B)  $\{ x \mid x \neq 3 , x \neq - 5 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3 , x \neq 5 \}$

Question 2

Graph the function.
-$$f ( x ) = x - \frac { 9 } { x }$$

Accepted Answer

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

Question 3

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }$$

Accepted Answer

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

Question 4

Solve the variation problem.
-The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth)and inversely as the orbital velocity. If a satellite completes an orbit 680 miles above the earth in 9 hours at a velocity of 23,000 mph, how long would it take a satellite to complete an orbit if it is at 1700 miles above the earth at a velocity of 28,000 mph? Use 3960 miles as the radius of the earth, and round your answer to the nearest hundredth of an hour.

Accepted Answer

A) 2.71 hours 
B) 9.02 hours 
C) 90.18 hours 
D) 18.48 hours 
A) 2.71 hours 
B) 9.02 hours 
C) 90.18 hours 
D) 18.48 hours

Question 5

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; x - 4$$

Accepted Answer

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

Question 6

Sketch the graph of the quadratic function.
-$ f(x)=-4(x-6)^{2}-2 $

Accepted Answer

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

Question 7

Sketch the graph of the polynomial function.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }$$

Accepted Answer

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

Question 8

Find the range of the quadratic function in interval notation.
-$$f ( x ) = 4 x ^ { 2 } - 2 x - 9$$

Accepted Answer

A)  $\left[ \frac { 1 } { 4 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 37 } { 4 } \right]$ 
C)  $\left[ - \frac { 37 } { 4 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 1 } { 4 } \right]$ 
A)  $\left[ \frac { 1 } { 4 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 37 } { 4 } \right]$ 
C)  $\left[ - \frac { 37 } { 4 } , \infty \right)$ 
D)  $\left( - \infty , \frac { 1 } { 4 } \right]$

Question 9

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
-$f ( x ) = x ^ { 2 } + 18 x + 66 \quad$ Give your answers in exact form.

Accepted Answer

A)  x-intercepts: $- 9 - \sqrt { 15 }$ and $- 9 + \sqrt { 15 } ; y$-intercept: 66 
B)  x-intercepts: $- 18 - \sqrt { 66 }$ and $- 18 + \sqrt { 66 } ;$ y-intercept: $- 66$ 
C)  x-intercepts: $9 - \sqrt { 66 }$ and $9 + \sqrt { 66 } ; y$-intercept: 66 
D)  $x$-intercepts: $9 + \sqrt { 15 } ; y$-intercept: $- 66$ 
A)  x-intercepts: $- 9 - \sqrt { 15 }$ and $- 9 + \sqrt { 15 } ; y$-intercept: 66 
B)  x-intercepts: $- 18 - \sqrt { 66 }$ and $- 18 + \sqrt { 66 } ;$ y-intercept: $- 66$ 
C)  x-intercepts: $9 - \sqrt { 66 }$ and $9 + \sqrt { 66 } ; y$-intercept: 66 
D)  $x$-intercepts: $9 + \sqrt { 15 } ; y$-intercept: $- 66$

Question 10

Find the range of the quadratic function in interval notation.
-$$f ( x ) = ( x + 4 ) ^ { 2 } - 9$$

Accepted Answer

A)  $[ - 4 , \infty )$ 
B)  $( - \infty , - 4 ]$ 
C)  $( - \infty , - 9 ]$ 
D)  $[ - 9 , \infty )$ 
A)  $[ - 4 , \infty )$ 
B)  $( - \infty , - 4 ]$ 
C)  $( - \infty , - 9 ]$ 
D)  $[ - 9 , \infty )$

Question 11

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-

Accepted Answer

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

Question 12

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
-$$f ( x ) = x ^ { 2 } + 2 x - 8$$

Accepted Answer

A)  vertex $( 1,9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0,8 )$
  
B)  vertex $( 1 , - 9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0 , - 8 )$
  
C)  vertex $( - 1 , - 9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0 , - 8 )$
  
D)  vertex $( - 1,9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0,8 )$
  
A)  vertex $( 1,9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0,8 )$
  
B)  vertex $( 1 , - 9 )$
intercepts $( - 2,0 ) , ( 4,0 ) , ( 0 , - 8 )$
  
C)  vertex $( - 1 , - 9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0 , - 8 )$
  
D)  vertex $( - 1,9 )$
intercepts $( 2,0 ) , ( - 4,0 ) , ( 0,8 )$

Question 13

Solve the polynomial equation in the complex numbers.
-$$x ^ { 3 } + 8 x ^ { 2 } + 16 x + 8 = 0$$

Accepted Answer

A)  $\{ 1 , - 1 , - 8 \}$ 
B)  $\{ 2 , - 6 + \sqrt { 5 } , - 6 - \sqrt { 5 } \}$ 
C)  $\{ - 2 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$ 
D)  $\{ - 2 , - 6 + \sqrt { 8 } , - 6 - \sqrt { 8 } \}$ 
A)  $\{ 1 , - 1 , - 8 \}$ 
B)  $\{ 2 , - 6 + \sqrt { 5 } , - 6 - \sqrt { 5 } \}$ 
C)  $\{ - 2 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$ 
D)  $\{ - 2 , - 6 + \sqrt { 8 } , - 6 - \sqrt { 8 } \}$

Question 14

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
-$$f ( x ) = x ^ { 2 } + 12 x + 36$$

Accepted Answer

A) x-intercepts: 6; y-intercept: 36 
B) No x-intercepts; y-intercept: 72 
C) x-intercepts: -6; y-intercept: 36 
D) x-intercepts: -6; y-intercept: 72 
A) x-intercepts: 6; y-intercept: 36 
B) No x-intercepts; y-intercept: 72 
C) x-intercepts: -6; y-intercept: 36 
D) x-intercepts: -6; y-intercept: 72

Question 15

Find the axis of symmetry of the quadratic function.
-$$f ( x ) = - x ^ { 2 } - 4 x + 6$$

Accepted Answer

A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = - 4$ 
D)  $x = 10$ 
A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = - 4$ 
D)  $x = 10$

Question 16

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6$$

Accepted Answer

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

Question 17

Rewrite the quadratic function in standard form by completing the square.
-$$f ( x ) = x ^ { 2 } - 6 x + 7$$

Accepted Answer

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

Question 18

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
-$ f(x)=-x^{2}+6 x-8 $

Accepted Answer

A)  vertex $( 3 , - 1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0,8 )$
  
B)  vertex $( - 3 , - 1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0,8 )$
  
C)  vertex $( 3,1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0 , - 8 )$
  
D)  vertex $( - 3,1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0 , - 8 )$
  
A)  vertex $( 3 , - 1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0,8 )$
  
B)  vertex $( - 3 , - 1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0,8 )$
  
C)  vertex $( 3,1 )$
intercepts $( 4,0 ) , ( 2,0 ) , ( 0 , - 8 )$
  
D)  vertex $( - 3,1 )$
intercepts $( - 4,0 ) , ( - 2,0 ) , ( 0 , - 8 )$

Question 19

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = 4 x ^ { 2 } + 8 x$$

Accepted Answer

A)  minimum at $( - 1 , - 4 )$ 
B)  maximum at $( 1 , - 4 )$ 
C)  minimum; (ii) $( 1 , - 4 )$ 
D)  maximum at $( - 1 , - 4 )$ 
A)  minimum at $( - 1 , - 4 )$ 
B)  maximum at $( 1 , - 4 )$ 
C)  minimum; (ii) $( 1 , - 4 )$ 
D)  maximum at $( - 1 , - 4 )$

Question 20

Give the equation of the slant asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } - 6 x + 3 } { x + 7 }$$

Accepted Answer

A) y = x + 9 
B) none 
C) y = x - 13 
D) x = y + 6 
A) y = x + 9 
B) none 
C) y = x - 13 
D) x = y + 6

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Graph the function. - $f ( x ) = x - \frac { 9 } { x }$ $Graph the function. - f ( x ) = x - \frac { 9 } { x }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; x - 4$

Sketch the graph of the quadratic function. - $f(x)=-4(x-6)^{2}-2$ $Sketch the graph of the quadratic function. - f(x)=-4(x-6)^{2}-2$

Sketch the graph of the polynomial function. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }$

Find the range of the quadratic function in interval notation. - $f ( x ) = 4 x ^ { 2 } - 2 x - 9$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 18 x + 66 \quad$ Give your answers in exact form.

Find the range of the quadratic function in interval notation. - $f ( x ) = ( x + 4 ) ^ { 2 } - 9$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = x ^ { 2 } + 2 x - 8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = x ^ { 2 } + 2 x - 8$

Solve the polynomial equation in the complex numbers. - $x ^ { 3 } + 8 x ^ { 2 } + 16 x + 8 = 0$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 12 x + 36$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - x ^ { 2 } - 4 x + 6$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 6 x + 7$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=-x^{2}+6 x-8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=-x^{2}+6 x-8$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 4 x ^ { 2 } + 8 x$

Give the equation of the slant asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } - 6 x + 3 } { x + 7 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 4: Polynomial and Rational Functions

Find the domain of the rational function. - f(x)=2x2−43x2+6x−45f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }f(x)=3x2+6x−452x2−4​

Graph the function. - f(x)=x−9xf ( x ) = x - \frac { 9 } { x }f(x)=x−x9​

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=−12x4f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }f(x)=−21​x4

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x3+2x2−6x+8;x−4f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; x - 4f(x)=x3+2x2−6x+8;x−4

Sketch the graph of the quadratic function. - f(x)=−4(x−6)2−2 f(x)=-4(x-6)^{2}-2 f(x)=−4(x−6)2−2

Sketch the graph of the polynomial function. - f(x)=x4−6x3+9x2f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }f(x)=x4−6x3+9x2

Find the range of the quadratic function in interval notation. - f(x)=4x2−2x−9f ( x ) = 4 x ^ { 2 } - 2 x - 9f(x)=4x2−2x−9

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=x2+18x+66f ( x ) = x ^ { 2 } + 18 x + 66 \quadf(x)=x2+18x+66 Give your answers in exact form.

Find the range of the quadratic function in interval notation. - f(x)=(x+4)2−9f ( x ) = ( x + 4 ) ^ { 2 } - 9f(x)=(x+4)2−9

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x2+2x−8f ( x ) = x ^ { 2 } + 2 x - 8f(x)=x2+2x−8

Solve the polynomial equation in the complex numbers. - x3+8x2+16x+8=0x ^ { 3 } + 8 x ^ { 2 } + 16 x + 8 = 0x3+8x2+16x+8=0

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=x2+12x+36f ( x ) = x ^ { 2 } + 12 x + 36f(x)=x2+12x+36

Find the axis of symmetry of the quadratic function. - f(x)=−x2−4x+6f ( x ) = - x ^ { 2 } - 4 x + 6f(x)=−x2−4x+6

Use the Factor Theorem to determine whether x - c is a factor of f(x). - (x)=x3+4x2−10x+12;x+6( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6(x)=x3+4x2−10x+12;x+6

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2−6x+7f ( x ) = x ^ { 2 } - 6 x + 7f(x)=x2−6x+7

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=−x2+6x−8 f(x)=-x^{2}+6 x-8 f(x)=−x2+6x−8

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - f(x)=4x2+8xf ( x ) = 4 x ^ { 2 } + 8 xf(x)=4x2+8x

Give the equation of the slant asymptote, if any, of the function. - f(x)=x2−6x+3x+7f ( x ) = \frac { x ^ { 2 } - 6 x + 3 } { x + 7 }f(x)=x+7x2−6x+3​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Graph the function. - $f ( x ) = x - \frac { 9 } { x }$ $Graph the function. - f ( x ) = x - \frac { 9 } { x }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 2 } x ^ { 4 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 ; x - 4$

Sketch the graph of the quadratic function. - $f(x)=-4(x-6)^{2}-2$ $Sketch the graph of the quadratic function. - f(x)=-4(x-6)^{2}-2$

Sketch the graph of the polynomial function. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 9 x ^ { 2 }$

Find the range of the quadratic function in interval notation. - $f ( x ) = 4 x ^ { 2 } - 2 x - 9$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 18 x + 66 \quad$ Give your answers in exact form.

Find the range of the quadratic function in interval notation. - $f ( x ) = ( x + 4 ) ^ { 2 } - 9$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = x ^ { 2 } + 2 x - 8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = x ^ { 2 } + 2 x - 8$

Solve the polynomial equation in the complex numbers. - $x ^ { 3 } + 8 x ^ { 2 } + 16 x + 8 = 0$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 12 x + 36$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - x ^ { 2 } - 4 x + 6$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $( x ) = x ^ { 3 } + 4 x ^ { 2 } - 10 x + 12 ; x + 6$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 6 x + 7$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=-x^{2}+6 x-8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=-x^{2}+6 x-8$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 4 x ^ { 2 } + 8 x$

Give the equation of the slant asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } - 6 x + 3 } { x + 7 }$