# Find the domain of the function

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