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Ma 105 Week 6 Assignment 20/20 Correct Answers

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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

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