Question 1

Find the domain of $f ( x ) = \frac { 2 x ^ { 2 } - x - 25 } { x ^ { 2 } + 5 x + 5 }$ .

Accepted Answer

A) all real numbers 
B) all real numbers except x = -5 
C) all real numbers except x = 25 
D) all real numbers except x = -1 
E) all real numbers except x = -5 and x = -2 
A) all real numbers 
B) all real numbers except x = -5 
C) all real numbers except x = 25 
D) all real numbers except x = -1 
E) all real numbers except x = -5 and x = -2

Question 2

Find the domain of the function and identify any vertical and horizontal asymptotes. 
 $f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$

Accepted Answer

A) The domain is all real numbers x except x = ±2. There is a vertical asymptote at x = -2, and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±2. There is a vertical asymptote at x = -2, and a horizontal asymptote at y = $\frac { 1 } { 2 }$ . 
C) The domain is all real numbers x. There is a vertical asymptote at x = -4, and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x  = ±4. There is a vertical asymptote at x = -4, and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x  = ±4. There is a vertical asymptote at x = -2, and no horizontal asymptote. 
A) The domain is all real numbers x except x = ±2. There is a vertical asymptote at x = -2, and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±2. There is a vertical asymptote at x = -2, and a horizontal asymptote at y = $\frac { 1 } { 2 }$ . 
C) The domain is all real numbers x. There is a vertical asymptote at x = -4, and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x  = ±4. There is a vertical asymptote at x = -4, and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x  = ±4. There is a vertical asymptote at x = -2, and no horizontal asymptote.

Question 3

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

Accepted Answer

A) -1 
B)  -i 
C)  1 
D)  i 
E) 5 
A) -1 
B)  -i 
C)  1 
D)  i 
E) 5

Question 4

In a pilot project, a rural township is given recycling bins for separating and storing recyclable products.The cost C (in dollars) of supplying bins to p% of the population is given by   $C = \frac { 42,000 p } { 100 - p } , 0 \leq p < 100$  
Select the correct graph of the cost function.

Accepted Answer

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

Question 5

Use long division to divide. 
 $2 x ^ { 2 } + 14 x + 20 \div x + 5$

Accepted Answer

A)  $2 x - 4 , x \neq - 5$ 
B)  $2 x + 4 , x \neq - 5$ 
C)  $2 x ^ { 2 } - 4 , x \neq - 5$ 
D)  $2 x ^ { 2 } + 4 , x \neq - 5$ 
E)  $2 x ^ { 2 } + 4 x , x \neq - 5$ 
A)  $2 x - 4 , x \neq - 5$ 
B)  $2 x + 4 , x \neq - 5$ 
C)  $2 x ^ { 2 } - 4 , x \neq - 5$ 
D)  $2 x ^ { 2 } + 4 , x \neq - 5$ 
E)  $2 x ^ { 2 } + 4 x , x \neq - 5$

Question 6

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

Accepted Answer

A) all real numbers except x = -2 
B) all real numbers 
C) all real numbers except x = -2 and x = 2 
D) all real numbers except x = 4 
E) all real numbers except x = 2 
A) all real numbers except x = -2 
B) all real numbers 
C) all real numbers except x = -2 and x = 2 
D) all real numbers except x = 4 
E) all real numbers except x = 2

Question 7

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry.

Accepted Answer

A)     Vertex: (-4, 5)Axis of symmetry: x = -4 
B)      Vertex: (-4, 1)Axis of symmetry: x = -4 
C)      Vertex: (-4, 2)Axis of symmetry: x = -4 
D)     Vertex: (-4, 4)Axis of symmetry: x = -4 
E)    Vertex: (-4, 3)Axis of symmetry: x = -4 
A)     Vertex: (-4, 5)Axis of symmetry: x = -4 
B)      Vertex: (-4, 1)Axis of symmetry: x = -4 
C)      Vertex: (-4, 2)Axis of symmetry: x = -4 
D)     Vertex: (-4, 4)Axis of symmetry: x = -4 
E)    Vertex: (-4, 3)Axis of symmetry: x = -4

Question 8

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }$

Accepted Answer

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

Question 9

Write the complex number in standard form. ​
-4i + i2
​

Accepted Answer

A) ​-1 + 4i 
B) ​-1 + 7i 
C) ​1 + 4i 
D) ​1 - 4i 
E) ​-1 - 4i 
A) ​-1 + 4i 
B) ​-1 + 7i 
C) ​1 + 4i 
D) ​1 - 4i 
E) ​-1 - 4i

Question 10

Graph the polynomial function. 
 $y = x ^ { 3 } + 5 x ^ { 2 }$

Accepted Answer

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

Question 11

Select the graph of $y = x ^ { 6 }$ and the transformation $f ( x ) = ( x + 3 ) ^ { 6 }$ .

Accepted Answer

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

Question 12

Given -6i is a root, determine all other roots of f(x) = x3 + 2x2 + 36x + 72. ​

Accepted Answer

A) x = -2, ±6 
B) x = -2, 6i 
C) x = -6, ±2i 
D) x = ±2, 6i 
E) x = ±2, 6 
A) x = -2, ±6 
B) x = -2, 6i 
C) x = -6, ±2i 
D) x = ±2, 6i 
E) x = ±2, 6

Question 13

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical.   $f ( x ) = x ^ { 3 } - 4 x + 1$ , $g ( x ) = x ^ { 3 }$

Accepted Answer

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

Question 14

Find the vertex of the parabola.
​
y = x2 + 14x + 49
​
Please enter your answer as an ordered pair.

Accepted Answer

Question 15

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.
  $h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )$

Accepted Answer

A) -18 
B) -17 
C) -21 
D) -15 
E) -19 
A) -18 
B) -17 
C) -21 
D) -15 
E) -19

Question 16

Find all the zeros of the function and write the polynomial as a product of linear factors. ​
Y4 - 2401
​

Accepted Answer

A) ±7; (y - 7)(y + 7) 
B) ±7, ±7i; (y - 7)(y + 7)(y - 7i)(y + 7i) 
C) 7, 7i; (y + 7)(y + 7)(y - 7i)(y - 7i) 
D) ±7i; (y - 7i)(y + 7i) 
E) ±7, ±7i; (y - 7)(y - 7)(y + 7i)(y + 7i) 
A) ±7; (y - 7)(y + 7) 
B) ±7, ±7i; (y - 7)(y + 7)(y - 7i)(y + 7i) 
C) 7, 7i; (y + 7)(y + 7)(y - 7i)(y - 7i) 
D) ±7i; (y - 7i)(y + 7i) 
E) ±7, ±7i; (y - 7)(y - 7)(y + 7i)(y + 7i)

Question 17

Given $f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5$ .Determine the domains of f(x) and g(x).

Accepted Answer

A) Domain of f(x): all real numbers except -5Domain of g(x): all real numbers except 5 
B) Domain of f(x): all real numbersDomain of g(x): all real numbers except 5 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -5Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 5Domain of g(x): all real numbers 
A) Domain of f(x): all real numbers except -5Domain of g(x): all real numbers except 5 
B) Domain of f(x): all real numbersDomain of g(x): all real numbers except 5 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except -5Domain of g(x): all real numbers 
E) Domain of f(x): all real numbers except 5Domain of g(x): all real numbers

Question 18

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }$ .

Accepted Answer

A) Domain: all real numbers except x = 5 and -4 
B) Domain: all real numbers except x = -5 and -4 
C) Domain: all real numbers except x = -5 and 4 
D) Domain: all real numbers except x = -4 
E) Domain: all real numbers 
A) Domain: all real numbers except x = 5 and -4 
B) Domain: all real numbers except x = -5 and -4 
C) Domain: all real numbers except x = -5 and 4 
D) Domain: all real numbers except x = -4 
E) Domain: all real numbers

Question 19

Find the zeros (if any) of the rational function.   $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }$

Accepted Answer

A) 8 
B) -8 
C)  2 
D) -1 
E) - 2 
A) 8 
B) -8 
C)  2 
D) -1 
E) - 2

Question 20

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

Accepted Answer

A) all real numbers except x = -6 and x = -5 
B) all real numbers except x = -1, x = 1, x = -6 and x = -5 
C) all real numbers except x = 6 
D) all real numbers except x = -1, x = 1 and x = -6 
E) all real numbers 
A) all real numbers except x = -6 and x = -5 
B) all real numbers except x = -1, x = 1, x = -6 and x = -5 
C) all real numbers except x = 6 
D) all real numbers except x = -1, x = 1 and x = -6 
E) all real numbers

Find the domain of $f ( x ) = \frac { 2 x ^ { 2 } - x - 25 } { x ^ { 2 } + 5 x + 5 }$ .

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$

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

In a pilot project, a rural township is given recycling bins for separating and storing recyclable products.The cost C (in dollars) of supplying bins to p% of the population is given by $C = \frac { 42,000 p } { 100 - p } , 0 \leq p < 100$ Select the correct graph of the cost function.

Use long division to divide. $2 x ^ { 2 } + 14 x + 20 \div x + 5$

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

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry.

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }$

Write the complex number in standard form. -4i + i²

Graph the polynomial function. $y = x ^ { 3 } + 5 x ^ { 2 }$

Select the graph of $y = x ^ { 6 }$ and the transformation $f ( x ) = ( x + 3 ) ^ { 6 }$ .

Given -6i is a root, determine all other roots of f(x) = x³ + 2x² + 36x + 72.

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical. $f ( x ) = x ^ { 3 } - 4 x + 1$ , $g ( x ) = x ^ { 3 }$

Find the vertex of the parabola. y = x² + 14x + 49 Please enter your answer as an ordered pair.

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )$

Find all the zeros of the function and write the polynomial as a product of linear factors. Y⁴ - 2401

Given $f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5$ .Determine the domains of f(x) and g(x).

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }$ .

Find the zeros (if any) of the rational function. $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .

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

Find the domain of f(x)=2x2−x−25x2+5x+5f ( x ) = \frac { 2 x ^ { 2 } - x - 25 } { x ^ { 2 } + 5 x + 5 }f(x)=x2+5x+52x2−x−25​ .

Find the domain of the function and identify any vertical and horizontal asymptotes. f(x)=x−2x2−4f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }f(x)=x2−4x−2​

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

Use long division to divide. 2x2+14x+20÷x+52 x ^ { 2 } + 14 x + 20 \div x + 52x2+14x+20÷x+5

Find the domain of f(x)=x+2x2−4f ( x ) = \frac { x + 2 } { x ^ { 2 } - 4 }f(x)=x2−4x+2​ .

Select the graph of the quadratic function f(x)=(x+4)2+3f ( x ) = ( x + 4 ) ^ { 2 } + 3f(x)=(x+4)2+3 .Identify the vertex and axis of symmetry.

Select the correct graph of the following function. f(x)=x26x+1f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }f(x)=6x+1x2​

Write the complex number in standard form. ​ -4i + i2 ​

Graph the polynomial function. y=x3+5x2y = x ^ { 3 } + 5 x ^ { 2 }y=x3+5x2

Select the graph of y=x6y = x ^ { 6 }y=x6 and the transformation f(x)=(x+3)6f ( x ) = ( x + 3 ) ^ { 6 }f(x)=(x+3)6 .

Given -6i is a root, determine all other roots of f(x) = x3 + 2x2 + 36x + 72. ​

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical. f(x)=x3−4x+1f ( x ) = x ^ { 3 } - 4 x + 1f(x)=x3−4x+1 , g(x)=x3g ( x ) = x ^ { 3 }g(x)=x3

Find the vertex of the parabola. ​ y = x2 + 14x + 49 ​ Please enter your answer as an ordered pair.

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. h(x)=x3−4x2−9x+7,h(2)h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )h(x)=x3−4x2−9x+7,h(2)

Find all the zeros of the function and write the polynomial as a product of linear factors. ​ Y4 - 2401 ​

Given f(x)=x2+25x+5,g(x)=x−5f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5f(x)=x+5x2+25​,g(x)=x−5 .Determine the domains of f(x) and g(x).

Determine the domain of the function f(x)=x2−25x2+x−20f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }f(x)=x2+x−20x2−25​ .

Find the zeros (if any) of the rational function. g(x)=x3−8x2+1g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }g(x)=x2+1x3−8​

Determine the domain of f(x)=x2+11x+30x3+6x2−x−6f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }f(x)=x3+6x2−x−6x2+11x+30​ .

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

Find the domain of $f ( x ) = \frac { 2 x ^ { 2 } - x - 25 } { x ^ { 2 } + 5 x + 5 }$ .

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x - 2 } { x ^ { 2 } - 4 }$

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

Use long division to divide. $2 x ^ { 2 } + 14 x + 20 \div x + 5$

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

Select the graph of the quadratic function $f ( x ) = ( x + 4 ) ^ { 2 } + 3$ .Identify the vertex and axis of symmetry.

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } } { 6 x + 1 }$

Write the complex number in standard form. -4i + i²

Graph the polynomial function. $y = x ^ { 3 } + 5 x ^ { 2 }$

Select the graph of $y = x ^ { 6 }$ and the transformation $f ( x ) = ( x + 3 ) ^ { 6 }$ .

Given -6i is a root, determine all other roots of f(x) = x³ + 2x² + 36x + 72.

Select the correct graph of the functions f and g in the same viewing window.Zoom out sufficiently far to show that the right-hand and left-hand behaviors of f and g appear identical. $f ( x ) = x ^ { 3 } - 4 x + 1$ , $g ( x ) = x ^ { 3 }$

Find the vertex of the parabola. y = x² + 14x + 49 Please enter your answer as an ordered pair.

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $h ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 9 x + 7 , \quad h ( 2 )$

Find all the zeros of the function and write the polynomial as a product of linear factors. Y⁴ - 2401

Given $f ( x ) = \frac { x ^ { 2 } + 25 } { x + 5 } , g ( x ) = x - 5$ .Determine the domains of f(x) and g(x).

Determine the domain of the function $f ( x ) = \frac { x ^ { 2 } - 25 } { x ^ { 2 } + x - 20 }$ .

Find the zeros (if any) of the rational function. $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 1 }$

Determine the domain of $f ( x ) = \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 3 } + 6 x ^ { 2 } - x - 6 }$ .