MA 105 Week 6 Assignment 20/20 Correct Answers

 

QUESTION 1

 

Find the domain of the function

 

    Domain: all real numbers x except x=6
    Domain: all real numbers x except x=8
    Domain: all real numbers x except x = -8
    Domain: all real numbers x
    Domain: all real numbers x except x = -6

 

QUESTION 2

 

Find the domain of the function

 

    Domain: all real numbers x except x = 7
    Domain:  all real numbers x except x = ±49
    Domain: all real numbers x except x = ±8
    Domain: all real numbers x except x = -7
    Domain: all real numbers x except x = ±7

 

QUESTION 3

 

Determine the domains of f and g.

 

    Domain of f: all real numbers x except x = -6

Domain of g: all real numbers x

    Domain of f: all real numbers x except x = ±6

Domain of g: all real numbers x

    Domain of f: all real numbers x except x = ±36

Domain of g: all real numbers x except x=6

    Domain of f: all real numbers x except x = 6

Domain of g: all real numbers x

    Domain of f: all real numbers x except x = ±6

Domain of g: all real numbers x except x=6

 

QUESTION 4

 

Find the domain of

 

    all real numbers except x = -9
    all real numbers except x = 81
    all real numbers except x = 9
    all real numbers except x = 9 and x = -9
    all real numbers

 

 

QUESTION 5

 

Find the domain of the function and identify any vertical and horizontal asymptotes.

 

    Domain: all real numbers x except x = 2

Vertical asymptote: x = 2

Horizontal asymptote: y = -1

    Domain: all real numbers x

Vertical asymptote: x = -2

Horizontal asymptote: y = 0

    Domain: all real numbers x except x = 0

Vertical asymptote: x = 0

Horizontal asymptote: y = -1

    Domain: all real numbers x except x = 2

Vertical asymptote: x = 0

Horizontal asymptote: y = -2

    Domain: all real numbers x except x = -2

Vertical asymptote: x = 0

Horizontal asymptote: y = 2

 

 QUESTION 6

 

Find the domain of the function and identify any vertical and horizontal asymptotes.

 

    Domain: all real numbers x except x = 0

Vertical asymptote: x = 0

Horizontal asymptote: y = -2

    Domain: all real numbers x except x = -6

Vertical asymptote: x = -6

Horizontal asymptote: No horizontal asymptote

    Domain: all real numbers x except x = 6

Vertical asymptote: x = 6

Horizontal asymptote: No horizontal asymptote

    Domain: all real numbers x except x = 6

Vertical asymptote: x = 6

Horizontal asymptote: y = 2

    Domain: all real numbers x

Vertical asymptote: x = -6

Horizontal asymptote: y = 0

 

QUESTION 7

 

Find the domain of the function and identify any vertical and horizontal asymptotes

.

    Domain: all real numbers x

Vertical asymptote: No vertical asymptote

Horizontal asymptote: y = 9

    Domain: all real numbers x except x = 0

Vertical asymptote: x = 0

Horizontal asymptote: y = -8

    Domain: all real numbers x

Vertical asymptote: x = -9

Horizontal asymptote: y = 0

    Domain: all real numbers x except x = 9

Vertical asymptote: No vertical asymptote

Horizontal asymptote: No horizontal asymptote

    Domain: all real numbers x except x = 9

Vertical asymptote: x = 9

Horizontal asymptote: y = 8

 

QUESTION 8

 

Determine the value that the function f approaches as the magnitude of x increases.

 

   
    -3
    2
    -1
    0

 

QUESTION 9

 

Simplify f and find any vertical asymptotes of f.

 

    x+6; Vertical asymptote: none
    x-6; Vertical asymptote: x=6
    x-6; Vertical asymptote: none
    x-36; Vertical asymptote: x=6
    x-36; Vertical asymptote: none

 

QUESTION 10

 

Simplify f and find any vertical asymptotes of f.

 

    x+3; Vertical asymptote: x = -3
    x; Vertical asymptote: none
    x; Vertical asymptote; x = -3
    x – 3; Vertical asymptote: none
    x2; Vertical asymptote: none

 

Determine the value that the function f approaches as the magnitude of x increases.

    3
    -3
    4
    -4
    -3.67

 

 

QUESTION 12

 

Find the domain of the function and identify any vertical and horizontal asymptotes.

 

    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.
    The domain is all real numbers x except x = ±2.  There is a vertical asymptote at x = -4, and a horizontal asymptote at y = 0.
    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.
    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.
    The domain is all real numbers x except x = ±4.  There is a vertical asymptote at x = -2, and a horizontal asymptote at y = 0.

 

QUESTION 13

 

Determine the equations of any horizontal and vertical asymptotes of

 

    horizontal: y = 5; vertical: x = 0
    horizontal: y = 1; vertical: x = -5
    horizontal: y=1; vertical: x=1 and x = -5
    horizontal: y = -1; vertical: x = -5
    horizontal: y = 0; vertical: none

 

 

QUESTION 14

Determine the equations of the vertical and horizontal asymptotes of the graph of the function.

 

    horizontal: x = -2; vertical: y = 3 and y = -3
    horizontal: y = 2; vertical: x = 3 and x = -3
    horizontal: y = -3; vertical: x = 2
    horizontal: y = 2; vertical: x = 3
    horizontal: x = 3 and x = -3; vertical: y = -2

 

 

QUESTION 15

Simplify f and find any vertical asymptotes of f.

 

    x2; Vertical asymptote: x = 0
    x-1: Vertical asymptote: none
    x: Vertical asymptote: x=0
    x:Vertical asymptote: none
    1/x: Vertical asymptote: x=0

 

 

QUESTION 16

 

Identify all intercepts of the function.

 

    y-intercept: (0,-1/4)
    y-intercept: (0,1/4)
    y-intercept: (0,4)
    y-intercept: (4,0)
    y-intercept: (0,-4)

 

 

QUESTION 17

Identify all intercepts of the following function:

 

    x-intercepts: (±3,0)
    no intercepts
    x-intercepts: (-3,0)
    x-intercepts: (0,0)
    x-intercepts: (3,0)

 

 

QUESTION 18

 

Select the correct graph of the function

 

     
     
     
     
     

 

QUESTION 19

 

Select the graph of the rational function.  (Plotted additional solution points as needed.)

     
     
     
     
     

 

 

QUESTION 20

 

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by

According to this model, would it be possible to remove 100% of the pollutants?

 

    No. The function is undefined at P = 100.
    Yes