# 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