Find the domain of the function and identify any vertical

Question

QUESTION 1
Find the domain of the function f(x) = 8/ (x-6)

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 f(x) = 8x² / (x² -49)

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.

f(x) = (x² -36) / (x + 6), g(x) = 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

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 f(x) = (x - 9) / (x² - 81)

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.

f(x) = (2 +x) / (2 -x)

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 asympotote: y = -2

Domain: all real numbers x except x = -2
Vertical asympotote: x = 0
Horizontal asympotote: y = 2

QUESTION 6
Find the domain of the function and identify any vertical and horizontal asympototes.

f(x) = 2x² / (x + 6)

Domain: all real numbers x except x = 0
Vertical asympotote: x = 0
Horizontal asympotote: y = -2

Domain: all real numbers x except x = -6
Vertical asympotote: x = -6
Horizontal asympotote: No horizontal asymptote

Domain: all real numbers x except x = 6
Vertical asympotote: x = 6
Horizontal asympotote: No horizontal asympotote

Domain: all real numbers x except x = 6
Vertical asympotote: 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 asympototes.

f(x) = (9x² + 8) / (9x² + x + 9)

Domain: all real numbers x
Vertical asympotote: 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.

f(x) = (2x - 1) / (x - 3)

∞

-3

2

-1

0

QUESTION 9
Simplify f and find any vertical asymptotes of f.

f(x) = (x² - 36) / (x + 6)

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.

f(x) = [x² (x + 3)] / (x² + 3x)

x+3; Vertical asymptote: x = -3

x; Vertical asymptote: none

x; Vertical asymptote; x = -3

x - 3; Vertical asympotote: none

x2; Vertical asympotote: none

QUESTION 11
Determine the value that the function f approaches as the magnitude of x increases.

f(x) = 4 - (3/x)

3

-3

4

-4

-3.67

QUESTION 12
Find the domain of the function and identify any vertical and horizontal asymptotes.

f(x) = (x + 2) / (x² - 4)

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

f(x) = (x² - 1) / (x² + 4x -5)

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.

f(x) = 2x² / (x² - 9)

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.

f(x) = (6x - 1) / (6x² - x)

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.

f(x) = 1 / (x - 4)

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:

g(x) = (x² +3) / x

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

f(x) = 6 / (x + 3)

QUESTION 19

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

g(x) = 1 / (2 -x)

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

C = 245p / (100 -p), 0 ≤ p < 100

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

No. The function is undefined at P = 100.

Yes