Question 1

Write the complex number in standard form. 
 $\sqrt { - 36 }$

Accepted Answer

A)  $\sqrt { 37 }$ i 
B) - $\sqrt { 39 }$ i 
C)  $6$ i 
D)  $\sqrt { 39 }$ i 
E) - $6$ i 
A)  $\sqrt { 37 }$ i 
B) - $\sqrt { 39 }$ i 
C)  $6$ i 
D)  $\sqrt { 39 }$ i 
E) - $6$ i C

Question 2

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by
  $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ .
 
Find the costs of removing 70% of the pollutants.
(Round your answer to two decimal places.)

Accepted Answer

A) $568.33 million 
B) $588.33 million 
C) $578.33 million 
D) $558.33 million 
E) $548.33 million 
A) $568.33 million 
B) $588.33 million 
C) $578.33 million 
D) $558.33 million 
E) $548.33 million E

Question 3

The graph of the function g(x) is a translation of the graph of f (x) = x 3.Graph the function g(x) = (x - 3) 3 - 1. ​

Accepted Answer

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

Question 4

Find real numbers a and b such that the equation is true.  
  $( a + 4 ) + 2 b i = 4 - 17 i$

Accepted Answer

A)  a = 0, b = - $\frac { 21 } { 2 }$ 
B)  a = 0, b = - $\frac { 17 } { 2 }$ 
C)  a = 0, b = - $\frac { 19 } { 2 }$ 
D)   a = 0, b = -9 
E)  a = 0, b = -10 
A)  a = 0, b = - $\frac { 21 } { 2 }$ 
B)  a = 0, b = - $\frac { 17 } { 2 }$ 
C)  a = 0, b = - $\frac { 19 } { 2 }$ 
D)   a = 0, b = -9 
E)  a = 0, b = -10

Question 5

Use long division to divide.  
  $( 4 x + 2 ) \div ( 2 x + 1 )$

Accepted Answer

A) 4 
B) 2 
C) -2 
D) 1 
E) 3 
A) 4 
B) 2 
C) -2 
D) 1 
E) 3

Question 6

Simplify the complex number and write it in standard form. 
 $- 42 i ^ { 5 }$

Accepted Answer

A)   $- 42 i ^ { 3 }$ 
B)   $42 i ^ { 3 }$ 
C)   $- 42 i$ 
D)   $- 42$ 
E)   $42 i$ 
A)   $- 42 i ^ { 3 }$ 
B)   $42 i ^ { 3 }$ 
C)   $- 42 i$ 
D)   $- 42$ 
E)   $42 i$

Question 7

Use long division to divide.   $\left( x ^ { 3 } + 343 \right) \div ( x + 7 )$

Accepted Answer

A)  $- x ^ { 2 } + 7 x + 49 , x \neq - 7$ 
B)  $x ^ { 2 } - 343 x + 49 , x \neq - 7$ 
C)  $x ^ { 2 } - 7 x - 49 , x \neq - 7$ 
D)  $x ^ { 2 } - 7 x + 49 , x \neq - 7$ 
E)  $x ^ { 2 } + 7 x - 49 , x \neq - 7$ 
A)  $- x ^ { 2 } + 7 x + 49 , x \neq - 7$ 
B)  $x ^ { 2 } - 343 x + 49 , x \neq - 7$ 
C)  $x ^ { 2 } - 7 x - 49 , x \neq - 7$ 
D)  $x ^ { 2 } - 7 x + 49 , x \neq - 7$ 
E)  $x ^ { 2 } + 7 x - 49 , x \neq - 7$

Question 8

Solve the inequality and graph the solution on the real number line. 
 $x ^ { 2 } < 4$

Accepted Answer

A)  $[ - 2,2 ]$   
B)  $[ - 2,2 ]$   
C)  $( - 2,2 )$     
D)  $( - 2,2 )$    
E)  $( - 2,2 )$     
A)  $[ - 2,2 ]$   
B)  $[ - 2,2 ]$   
C)  $( - 2,2 )$     
D)  $( - 2,2 )$    
E)  $( - 2,2 )$

Question 9

Graph the quadratic function. 
 $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$

Accepted Answer

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

Question 10

Use synthetic division to perform the division.
​ $\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }$

Accepted Answer

The answer of Use synthetic division to perform the division.
​...

Question 11

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

Accepted Answer

A)    Vertical shift. 
B)    Vertical shift. 
C)    Vertical shift. 
D)    Vertical shift. 
E)    Vertical shift. 
A)    Vertical shift. 
B)    Vertical shift. 
C)    Vertical shift. 
D)    Vertical shift. 
E)    Vertical shift.

Question 12

A bulk food storage bin with dimensions 3 feet by 4 feet by 5 feet needs to be increased in size to hold five times as much food as the current bin.(Assume each dimension is increased by the same amount.).Write a function that represents the volume of the new bin. ​

Accepted Answer

A) ​V(x) = x3 + 12x2 + 47x + 60 = -300 
B) V(x) = x3 + 12x2 + 47x + 60 = 300 
C) V(x) = x3 + 12x2 + 47x = 300 
D) V(x) = x3 + 12x2 - 47x - 60 = 300 
E) V(x) = x3 - 12x2 + 47x - 60 = 300 
A) ​V(x) = x3 + 12x2 + 47x + 60 = -300 
B) V(x) = x3 + 12x2 + 47x + 60 = 300 
C) V(x) = x3 + 12x2 + 47x = 300 
D) V(x) = x3 + 12x2 - 47x - 60 = 300 
E) V(x) = x3 - 12x2 + 47x - 60 = 300

Question 13

Solve the inequality and graph the solution on the real number line  
 $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$

Accepted Answer

A)  $( - \infty , 3 ]$   
B)  $( - \infty , 3 )$   
C)  $( - \infty , 3 ]$   
D)  $( - \infty , - 3 ]$   
E)  $( - \infty , - 3 )$   
A)  $( - \infty , 3 ]$   
B)  $( - \infty , 3 )$   
C)  $( - \infty , 3 ]$   
D)  $( - \infty , - 3 ]$   
E)  $( - \infty , - 3 )$

Question 14

Select the graph of the quadratic function $f ( x ) = 3 - x ^ { 2 }$ .Identify the vertex and axis of symmetry.

Accepted Answer

A)     Vertex: (0, 3)Axis of symmetry: y-axis 
B)     Vertex: (0, 1)Axis of symmetry: y-axis 
C)     Vertex: (0, 5)Axis of symmetry: y-axis 
D)     Vertex: (0, 4)Axis of symmetry: y-axis 
E)     Vertex: (0, 2)Axis of symmetry: y-axis 
A)     Vertex: (0, 3)Axis of symmetry: y-axis 
B)     Vertex: (0, 1)Axis of symmetry: y-axis 
C)     Vertex: (0, 5)Axis of symmetry: y-axis 
D)     Vertex: (0, 4)Axis of symmetry: y-axis 
E)     Vertex: (0, 2)Axis of symmetry: y-axis

Question 15

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window.

Accepted Answer

A)  $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$ 
B)  $A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$ 
C)  $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$ 
D)  $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$ 
E)  $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$ 
A)  $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 8 }$ 
B)  $A ( x ) = \frac { 80 x - x ^ { 2 } } { 2 }$ 
C)  $A ( x ) = \frac { 80 x - 2 x ^ { 2 } - \pi x ^ { 2 } } { 4 }$ 
D)  $A ( x ) = \frac { 80 x + ( 2 - \pi ) x ^ { 2 } } { 4 }$ 
E)  $A ( x ) = \frac { 160 x - 4 x ^ { 2 } - \pi x ^ { 2 } } { 2 }$

Question 16

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals.  
F(x) = x4 + 42x2 - 343

Accepted Answer

A)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )$ 
B)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x + \sqrt { 7 } )$ 
C)  $\left( x ^ { 2 } + 49 \right) ( x - \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
D)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
E)  $\left( x ^ { 2 } + 49 \right) ( x + 7 ) ( x - \sqrt { 7 } )$ 
A)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - 7 )$ 
B)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x + \sqrt { 7 } )$ 
C)  $\left( x ^ { 2 } + 49 \right) ( x - \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
D)  $\left( x ^ { 2 } + 49 \right) ( x + \sqrt { 7 } ) ( x - \sqrt { 7 } )$ 
E)  $\left( x ^ { 2 } + 49 \right) ( x + 7 ) ( x - \sqrt { 7 } )$

Question 17

Use long division to divide. $\left( x ^ { 3 } - 5 x - 3 \right) \div ( x - 2 )$

Accepted Answer

\[\begin{array} { l } 
x ^ { 2 } + 2 x -

Question 18

Select the correct graph of the following function.   $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5$

Accepted Answer

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

Question 19

Find the key numbers of the expression. 
 $16 x ^ { 3 } - 49 x ^ { 2 }$

Accepted Answer

A) 0, $\frac { 16 } { 49 }$ 
B) 0, 49 
C) 0, 51 
D) 0, -49 
E) 0, $\frac { 49 } { 16 }$ 
A) 0, $\frac { 16 } { 49 }$ 
B) 0, 49 
C) 0, 51 
D) 0, -49 
E) 0, $\frac { 49 } { 16 }$

Question 20

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.
 $f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )$

Accepted Answer

A) 94 
B) -94 
C) -90 
D) -91 
E) -89 
A) 94 
B) -94 
C) -90 
D) -91 
E) -89

Write the complex number in standard form. $\sqrt { - 36 }$

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ . Find the costs of removing 70% of the pollutants. (Round your answer to two decimal places.)

The graph of the function g(x) is a translation of the graph of f (x) = x ³.Graph the function g(x) = (x - 3) ³ - 1.

Find real numbers a and b such that the equation is true. $( a + 4 ) + 2 b i = 4 - 17 i$

Use long division to divide. $( 4 x + 2 ) \div ( 2 x + 1 )$

Simplify the complex number and write it in standard form. $- 42 i ^ { 5 }$

Use long division to divide. $\left( x ^ { 3 } + 343 \right) \div ( x + 7 )$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } < 4$

Graph the quadratic function. $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }$

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

A bulk food storage bin with dimensions 3 feet by 4 feet by 5 feet needs to be increased in size to hold five times as much food as the current bin.(Assume each dimension is increased by the same amount.).Write a function that represents the volume of the new bin.

Solve the inequality and graph the solution on the real number line $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$

Select the graph of the quadratic function $f ( x ) = 3 - x ^ { 2 }$ .Identify the vertex and axis of symmetry.

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. F(x) = x⁴ + 42x² - 343

Use long division to divide. $\left( x ^ { 3 } - 5 x - 3 \right) \div ( x - 2 )$

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5$

Find the key numbers of the expression. $16 x ^ { 3 } - 49 x ^ { 2 }$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )$

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

Write the complex number in standard form. −36\sqrt { - 36 }−36​

The graph of the function g(x) is a translation of the graph of f (x) = x 3.Graph the function g(x) = (x - 3) 3 - 1. ​

Find real numbers a and b such that the equation is true. (a+4)+2bi=4−17i( a + 4 ) + 2 b i = 4 - 17 i(a+4)+2bi=4−17i

Use long division to divide. (4x+2)÷(2x+1)( 4 x + 2 ) \div ( 2 x + 1 )(4x+2)÷(2x+1)

Simplify the complex number and write it in standard form. −42i5- 42 i ^ { 5 }−42i5

Use long division to divide. (x3+343)÷(x+7)\left( x ^ { 3 } + 343 \right) \div ( x + 7 )(x3+343)÷(x+7)

Solve the inequality and graph the solution on the real number line. x2<4x ^ { 2 } < 4x2<4

Graph the quadratic function. f(x)=−13x2−2f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2f(x)=−31​x2−2

Use synthetic division to perform the division. ​ 3x3+4x2+18x−25x−1\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }x−13x3+4x2+18x−25​

Select the graph of the function y=x2−1y = x ^ { 2 } - 1y=x2−1 .Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2 .

A bulk food storage bin with dimensions 3 feet by 4 feet by 5 feet needs to be increased in size to hold five times as much food as the current bin.(Assume each dimension is increased by the same amount.).Write a function that represents the volume of the new bin. ​

Solve the inequality and graph the solution on the real number line x3+3x2−9x−27≤0x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0x3+3x2−9x−27≤0

Select the graph of the quadratic function f(x)=3−x2f ( x ) = 3 - x ^ { 2 }f(x)=3−x2 .Identify the vertex and axis of symmetry.

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below.If the perimeter of the window is 40 ft, express the area, A, as a function of the width, x, of the window.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. F(x) = x4 + 42x2 - 343

Use long division to divide. (x3−5x−3)÷(x−2)\left( x ^ { 3 } - 5 x - 3 \right) \div ( x - 2 )(x3−5x−3)÷(x−2)

Select the correct graph of the following function. f(x)=6x3+x2−9x+5f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5f(x)=6x3+x2−9x+5

Find the key numbers of the expression. 16x3−49x216 x ^ { 3 } - 49 x ^ { 2 }16x3−49x2

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. f(x)=4x3−3x+8,f(−3)f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )f(x)=4x3−3x+8,f(−3)

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

Write the complex number in standard form. $\sqrt { - 36 }$

The graph of the function g(x) is a translation of the graph of f (x) = x ³.Graph the function g(x) = (x - 3) ³ - 1.

Find real numbers a and b such that the equation is true. $( a + 4 ) + 2 b i = 4 - 17 i$

Use long division to divide. $( 4 x + 2 ) \div ( 2 x + 1 )$

Simplify the complex number and write it in standard form. $- 42 i ^ { 5 }$

Use long division to divide. $\left( x ^ { 3 } + 343 \right) \div ( x + 7 )$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } < 4$

Graph the quadratic function. $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 } - 2$

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }$

Select the graph of the function $y = x ^ { 2 } - 1$ .Compare the graph of this function with the graph of $y = x ^ { 2 }$ .

A bulk food storage bin with dimensions 3 feet by 4 feet by 5 feet needs to be increased in size to hold five times as much food as the current bin.(Assume each dimension is increased by the same amount.).Write a function that represents the volume of the new bin.

Solve the inequality and graph the solution on the real number line $x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$

Select the graph of the quadratic function $f ( x ) = 3 - x ^ { 2 }$ .Identify the vertex and axis of symmetry.

Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. F(x) = x⁴ + 42x² - 343

Use long division to divide. $\left( x ^ { 3 } - 5 x - 3 \right) \div ( x - 2 )$

Select the correct graph of the following function. $f ( x ) = 6 x ^ { 3 } + x ^ { 2 } - 9 x + 5$

Find the key numbers of the expression. $16 x ^ { 3 } - 49 x ^ { 2 }$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 4 x ^ { 3 } - 3 x + 8 , f ( - 3 )$