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