Question 1

Solve the inequality and write the solution set in interval notation. 
$x ^ { 3 } - 36 x \geq 0$

Accepted Answer

A)  $[ - 6,0 ] \cup [ 6 , \infty ]$ 
B)  $[ - 6,0 ] \cup [ 6 , \infty )$ 
C)  $[ - 36,0 ] \cap [ 6 , \infty ]$ 
D)  $[ - 36,0 ] \cup [ - 6 , \infty )$ 
E)  $[ - 6,0 ] \cap [ 6 , \infty )$ 
A)  $[ - 6,0 ] \cup [ 6 , \infty ]$ 
B)  $[ - 6,0 ] \cup [ 6 , \infty )$ 
C)  $[ - 36,0 ] \cap [ 6 , \infty ]$ 
D)  $[ - 36,0 ] \cup [ - 6 , \infty )$ 
E)  $[ - 6,0 ] \cap [ 6 , \infty )$

Question 2

Select the correct graph of the following function. $f ( x ) = - \frac { 1 } { ( x - 3 ) ^ { 2 } }$

Accepted Answer

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

Question 3

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

Accepted Answer

A)  $x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1$ 
B)  $x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
C)  $x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1$ 
D)  $x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
E)  $x = - 3 \text {, multiplicity } 3$ 
A)  $x = 6 , \text { multiplicity } 2 ; x = - 3 \text {, multiplicity } 1$ 
B)  $x = 6 \text {, multiplicity } 1 ; x = - 6 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
C)  $x = - 3 \text {, multiplicity } 2 ; x = - 6 \text {, multiplicity } 1$ 
D)  $x = - 6 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$ 
E)  $x = - 3 \text {, multiplicity } 3$

Question 4

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .

Accepted Answer

A) x-intercept: none; y-intercept: none 
B) x-intercept: $\left( - \frac { 7 } { 5 } , 0 \right)$ ; y-intercept: none 
C) x-intercept: (-2, 0); y-intercept: (0, -2) 
D) x-intercepts: (-5, 0), (-1,0), (1, 0); y-intercept: (0, -2) 
E) x-intercept: (0, 0); y-intercept: (0, 0) 
A) x-intercept: none; y-intercept: none 
B) x-intercept: $\left( - \frac { 7 } { 5 } , 0 \right)$ ; y-intercept: none 
C) x-intercept: (-2, 0); y-intercept: (0, -2) 
D) x-intercepts: (-5, 0), (-1,0), (1, 0); y-intercept: (0, -2) 
E) x-intercept: (0, 0); y-intercept: (0, 0)

Question 5

Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Accepted Answer

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

Question 6

Find all the rational zeros of the function. ​
X3 - 7x2 + 14x - 8
​

Accepted Answer

A) -1, -2, -4 
B) 1, 2, 4 
C) 1, -2, 4 
D) -1, 2, 4 
E) ​-1, 2, -4 
A) -1, -2, -4 
B) 1, 2, 4 
C) 1, -2, 4 
D) -1, 2, 4 
E) ​-1, 2, -4

Question 7

Use synthetic division to perform the division. 
 $\frac { 3 x ^ { 3 } - 6 x ^ { 2 } - 23 x + 8 } { x + 2 }$

Accepted Answer

A)  $3 x ^ { 2 } - 12 x + 1 + \frac { 6 } { x + 2 }$ 
B)  $3 x ^ { 2 } - 12 x + 6 + \frac { 8 } { x + 2 }$ 
C)  $3 x ^ { 2 } - 12 x + 1$ 
D)  $x ^ { 2 } - 12 x + 3 - \frac { 6 } { x + 2 }$ 
E) none of these 
A)  $3 x ^ { 2 } - 12 x + 1 + \frac { 6 } { x + 2 }$ 
B)  $3 x ^ { 2 } - 12 x + 6 + \frac { 8 } { x + 2 }$ 
C)  $3 x ^ { 2 } - 12 x + 1$ 
D)  $x ^ { 2 } - 12 x + 3 - \frac { 6 } { x + 2 }$ 
E) none of these

Question 8

Do the operation and express the answer in a + bi form. 
 $( 9 - \sqrt { - 100 } ) + ( 10 + \sqrt { - 36 } )$

Accepted Answer

A) 19 - 4i 
B) - 38 - 8i 
C) 19 + 4i 
D) - 38 + 8i 
E) - 19 + 4i 
A) 19 - 4i 
B) - 38 - 8i 
C) 19 + 4i 
D) - 38 + 8i 
E) - 19 + 4i

Question 9

Find all rational roots of the equation.  
13x 3 - 2x 2 + 52x - 8 = 0

Accepted Answer

A)  $x = \frac { 2 } { 3 }$ 
B) x = -2i 
C) x = 2i 
D)  $x = - \frac { 2 } { 13 }$ 
E)   $x = \frac { 2 } { 13 }$ 
A)  $x = \frac { 2 } { 3 }$ 
B) x = -2i 
C) x = 2i 
D)  $x = - \frac { 2 } { 13 }$ 
E)   $x = \frac { 2 } { 13 }$

Question 10

Determine the zeros (if any) of the rational function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$ .

Accepted Answer

A) x = -6, x = 6 
B)  $x = - \sqrt { 6 } , x = \sqrt { 6 }$ 
C)  $x = - \frac { 1 } { 2 } , x = \frac { 1 } { 2 }$ 
D) x = -3 
E) no zeros 
A) x = -6, x = 6 
B)  $x = - \sqrt { 6 } , x = \sqrt { 6 }$ 
C)  $x = - \frac { 1 } { 2 } , x = \frac { 1 } { 2 }$ 
D) x = -3 
E) no zeros

Question 11

Select the correct graph of the function $f ( x ) = \frac { 8 } { x - 2 }$ .

Accepted Answer

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

Question 12

Use synthetic division to divide. $\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )$

Accepted Answer

A)   $x ^ { 2 } + 3 x - 18$ 
B)   $x ^ { 2 } - 3 x - 27$ 
C)   $x ^ { 2 } + 9 x + 18$ 
D)   $x ^ { 2 } + 9 x - 6$ 
E)   $x ^ { 2 } + 6 x + 9$ 
A)   $x ^ { 2 } + 3 x - 18$ 
B)   $x ^ { 2 } - 3 x - 27$ 
C)   $x ^ { 2 } + 9 x + 18$ 
D)   $x ^ { 2 } + 9 x - 6$ 
E)   $x ^ { 2 } + 6 x + 9$

Question 13

Simplify the complex number and write it in standard form. 
 $( \sqrt { - 57 } ) ^ { 3 }$

Accepted Answer

A) 185,193i 
B) -57i 
C) - $57 \sqrt { 57 }$ i 
D)  $57 \sqrt { 57 }$ i 
E) -185,193i 
A) 185,193i 
B) -57i 
C) - $57 \sqrt { 57 }$ i 
D)  $57 \sqrt { 57 }$ i 
E) -185,193i

Question 14

Determine the value that the function f approaches as the magnitude of x increases. 
 $f ( x ) = 2 - \frac { 4 } { x }$

Accepted Answer

A) 1 
B) -4 
C) 2 
D) -2 
E) -1.75 
A) 1 
B) -4 
C) 2 
D) -2 
E) -1.75

Question 15

Perform the operation and write the result in standard form.  
  $\frac { 3 } { 1 + i } - \frac { 4 } { 1 - i }$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ + $\frac { 2 } { 7 }$ i 
B)  $- \frac { 1 } { 2 }$ - $\frac { 2 } { 7 }$ i 
C)  $- \frac { 1 } { 2 }$ + $\frac { 7 } { 2 }$ i 
D)  $\frac { 7 } { 2 }$ $- \frac { 1 } { 2 }$ i 
E)  $- \frac { 1 } { 2 }$ - $\frac { 7 } { 2 }$ i 
A)  $- \frac { 1 } { 2 }$ + $\frac { 2 } { 7 }$ i 
B)  $- \frac { 1 } { 2 }$ - $\frac { 2 } { 7 }$ i 
C)  $- \frac { 1 } { 2 }$ + $\frac { 7 } { 2 }$ i 
D)  $\frac { 7 } { 2 }$ $- \frac { 1 } { 2 }$ i 
E)  $- \frac { 1 } { 2 }$ - $\frac { 7 } { 2 }$ i

Question 16

An open box is to be made from a square piece of cardboard, 24 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ , determine the domain of $$V ( x )$$ .

Accepted Answer

A) $D = \{ x \mid x > 0 \}$ B) $D = \{ x \mid 0 < x < 12 \}$ C) $D = \{ x \mid 48 < x < 96 \}$ D) $D = \{ x \mid 0 < x < 24 \}$ E) $D = \{ x \mid 12 < x < 24 \}$ A) $D = \{ x \mid x > 0 \}$ B) $D = \{ x \mid 0 < x < 12 \}$ C) $D = \{ x \mid 48 < x < 96 \}$ D) $D = \{ x \mid 0 < x < 24 \}$ E) $D = \{ x \mid 12 < x < 24 \}$

Solve the inequality and write the solution set in interval notation. $x ^ { 3 } - 36 x \geq 0$

Select the correct graph of the following function. $f ( x ) = - \frac { 1 } { ( x - 3 ) ^ { 2 } }$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .

Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Find all the rational zeros of the function. X³ - 7x² + 14x - 8

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } - 6 x ^ { 2 } - 23 x + 8 } { x + 2 }$

Do the operation and express the answer in a + bi form. $( 9 - \sqrt { - 100 } ) + ( 10 + \sqrt { - 36 } )$

Find all rational roots of the equation. 13x ³ - 2x ² + 52x - 8 = 0

Determine the zeros (if any) of the rational function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$ .

Select the correct graph of the function $f ( x ) = \frac { 8 } { x - 2 }$ .

Use synthetic division to divide. $\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )$

Simplify the complex number and write it in standard form. $( \sqrt { - 57 } ) ^ { 3 }$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

Perform the operation and write the result in standard form. $\frac { 3 } { 1 + i } - \frac { 4 } { 1 - i }$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Solve the inequality and write the solution set in interval notation. x3−36x≥0x ^ { 3 } - 36 x \geq 0x3−36x≥0

Select the correct graph of the following function. f(x)=−1(x−3)2f ( x ) = - \frac { 1 } { ( x - 3 ) ^ { 2 } }f(x)=−(x−3)21​

Find all real zeros of the polynomial f(x)=x3+3x2−36x−108f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108f(x)=x3+3x2−36x−108 and determine the multiplicity of each.

Identify all intercepts of f(x)=x2+7x+10x3+5x2−x−5f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }f(x)=x3+5x2−x−5x2+7x+10​ .

Select the correct graph of the function f(x)=6x+4f ( x ) = \frac { 6 } { x + 4 }f(x)=x+46​ .

Find all the rational zeros of the function. ​ X3 - 7x2 + 14x - 8 ​

Use synthetic division to perform the division. 3x3−6x2−23x+8x+2\frac { 3 x ^ { 3 } - 6 x ^ { 2 } - 23 x + 8 } { x + 2 }x+23x3−6x2−23x+8​

Do the operation and express the answer in a + bi form. (9−−100)+(10+−36)( 9 - \sqrt { - 100 } ) + ( 10 + \sqrt { - 36 } )(9−−100​)+(10+−36​)

Find all rational roots of the equation. 13x 3 - 2x 2 + 52x - 8 = 0

Determine the zeros (if any) of the rational function g(x)=6+3x2+6g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }g(x)=6+x2+63​ .

Select the correct graph of the function f(x)=8x−2f ( x ) = \frac { 8 } { x - 2 }f(x)=x−28​ .

Use synthetic division to divide. (x3−27x+54)÷(x−3)\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )(x3−27x+54)÷(x−3)

Simplify the complex number and write it in standard form. (−57)3( \sqrt { - 57 } ) ^ { 3 }(−57​)3

Determine the value that the function f approaches as the magnitude of x increases. f(x)=2−4xf ( x ) = 2 - \frac { 4 } { x }f(x)=2−x4​

Perform the operation and write the result in standard form. 31+i−41−i\frac { 3 } { 1 + i } - \frac { 4 } { 1 - i }1+i3​−1−i4​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Solve the inequality and write the solution set in interval notation. $x ^ { 3 } - 36 x \geq 0$

Select the correct graph of the following function. $f ( x ) = - \frac { 1 } { ( x - 3 ) ^ { 2 } }$

Find all real zeros of the polynomial $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 36 x - 108$ and determine the multiplicity of each.

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 3 } + 5 x ^ { 2 } - x - 5 }$ .

Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Find all the rational zeros of the function. X³ - 7x² + 14x - 8

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } - 6 x ^ { 2 } - 23 x + 8 } { x + 2 }$

Do the operation and express the answer in a + bi form. $( 9 - \sqrt { - 100 } ) + ( 10 + \sqrt { - 36 } )$

Find all rational roots of the equation. 13x ³ - 2x ² + 52x - 8 = 0

Determine the zeros (if any) of the rational function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$ .

Select the correct graph of the function $f ( x ) = \frac { 8 } { x - 2 }$ .

Use synthetic division to divide. $\left( x ^ { 3 } - 27 x + 54 \right) \div ( x - 3 )$

Simplify the complex number and write it in standard form. $( \sqrt { - 57 } ) ^ { 3 }$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

Perform the operation and write the result in standard form. $\frac { 3 } { 1 + i } - \frac { 4 } { 1 - i }$