Algebra Quiz : MA105

Question 1

Find the domain of the function

[removed]		Domain: all real numbers x except x=6
[removed]		Domain: all real numbers x except x=8
[removed]		Domain: all real numbers x except x = -8
[removed]		Domain: all real numbers x
[removed]		Domain: all real numbers x except x = -6

5 points

Question 2

Find the domain of the function

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

5 points

Question 3

Determine the domains of f and g.

[removed]		Domain of f: all real numbers x except x = -6 Domain of g: all real numbers x
[removed]		Domain of f: all real numbers x except x = ±6 Domain of g: all real numbers x
[removed]		Domain of f: all real numbers x except x = ±36 Domain of g: all real numbers x except x=6
[removed]		Domain of f: all real numbers x except x = 6 Domain of g: all real numbers x
[removed]		Domain of f: all real numbers x except x = ±6 Domain of g: all real numbers x except x=6

5 points

Question 4

Find the domain of

[removed]		all real numbers except x = -9
[removed]		all real numbers except x = 81
[removed]		all real numbers except x = 9
[removed]		all real numbers except x = 9 and x = -9
[removed]		all real numbers

5 points

Question 5

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

[removed]		Domain: all real numbers x except x = 2 Vertical asymptote: x = 2 Horizontal asymptote: y = -1
[removed]		Domain: all real numbers x Vertical asymptote: x = -2 Horizontal asymptote: y = 0
[removed]		Domain: all real numbers x except x = 0 Vertical asymptote: x = 0 Horizontal asymptote: y = -1
[removed]		Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asympotote: y = -2
[removed]		Domain: all real numbers x except x = -2 Vertical asympotote: x = 0 Horizontal asympotote: y = 2

5 points

Question 6

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

[removed]		Domain: all real numbers x except x = 0 Vertical asympotote: x = 0 Horizontal asympotote: y = -2
[removed]		Domain: all real numbers x except x = -6 Vertical asympotote: x = -6 Horizontal asympotote: No horizontal asymptote
[removed]		Domain: all real numbers x except x = 6 Vertical asympotote: x = 6 Horizontal asympotote: No horizontal asympotote
[removed]		Domain: all real numbers x except x = 6 Vertical asympotote: x = 6 Horizontal asymptote: y = 2
[removed]		Domain: all real numbers x Vertical asymptote: x = -6 Horizontal asymptote: y = 0

5 points

Question 7

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

[removed]		Domain: all real numbers x Vertical asympotote: No vertical asymptote Horizontal asymptote: y = 9
[removed]		Domain: all real numbers x except x = 0 Vertical asymptote: x = 0 Horizontal asymptote: y = -8
[removed]		Domain: all real numbers x Vertical asymptote: x = -9 Horizontal asymptote: y = 0
[removed]		Domain: all real numbers x except x = 9 Vertical asymptote: No vertical asymptote Horizontal asymptote: No horizontal asymptote
[removed]		Domain: all real numbers x except x = 9 Vertical asymptote: x = 9 Horizontal asymptote: y = 8

5 points

Question 8

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

[removed]		∞
[removed]		-3
[removed]		2
[removed]		-1
[removed]		0

5 points

Question 9

Simplify f and find any vertical asymptotes of f.

[removed]		x+6; Vertical asymptote: none
[removed]		x-6; Vertical asymptote: x=6
[removed]		x-6; Vertical asymptote: none
[removed]		x-36; Vertical asymptote: x=6
[removed]		x-36; Vertical asymptote: none

5 points

Question 10

Simplify f and find any vertical asymptotes of f.

[removed]		x+3; Vertical asymptote: x = -3
[removed]		x; Vertical asymptote: none
[removed]		x; Vertical asymptote; x = -3
[removed]		x - 3; Vertical asympotote: none
[removed]		x²; Vertical asympotote: none

5 points

Question 11

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

[removed]		3
[removed]		-3
[removed]		4
[removed]		-4
[removed]		-3.67

5 points

Question 12

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

[removed]		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.
[removed]		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.
[removed]		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.
[removed]		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.
[removed]		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.

5 points

Question 13

Determine the equations of any horizontal and vertical asymptotes of

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

5 points

Question 14

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

[removed]		horizontal: x = -2; vertical: y = 3 and y = -3
[removed]		horizontal: y = 2; vertical: x = 3 and x = -3
[removed]		horizontal: y = -3; vertical: x = 2
[removed]		horizontal: y = 2; vertical: x = 3
[removed]		horizontal: x = 3 and x = -3; vertical: y = -2

5 points

Question 15

Simplify f and find any vertical asymptotes of f.

[removed]		x²; Vertical asymptote: x = 0
[removed]		x-1: Vertical asymptote: none
[removed]		x: Vertical asymptote: x=0
[removed]		x:Vertical asymptote: none
[removed]		¹/_x: Vertical asymptote: x=0

5 points

Question 16

Identify all intercepts of the function.

[removed]		y-intercept: (0,-¹/₄)
[removed]		y-intercept: (0,¹/₄)
[removed]		y-intercept: (0,4)
[removed]		y-intercept: (4,0)
[removed]		y-intercept: (0,-4)

5 points

Question 17

Identify all intercepts of the following function:

[removed]		x-intercepts: (±3,0)
[removed]		no intercepts
[removed]		x-intercepts: (-3,0)
[removed]		x-intercepts: (0,0)
[removed]		x-intercepts: (3,0)

5 points

Question 18

Select the correct graph of the function

[removed]
[removed]
[removed]
[removed]
[removed]

5 points

Question 19

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

[removed]
[removed]
[removed]
[removed]
[removed]

5 points

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?

[removed]		No. The function is undefined at P = 100.
[removed]		Yes

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