QUESTION 1
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
5 points
QUESTION 2
1. 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
5 points
QUESTION 3
1. 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
5 points
QUESTION 4
1. 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
5 points
QUESTION 5
1. 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 asympotote: y = -2
Domain: all real numbers x except x = -2
Vertical asympotote: x = 0
Horizontal asympotote: y = 2
5 points
QUESTION 6
1. Find the domain of the function and identify any vertical and horizontal asympototes.
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
5 points
QUESTION 7
1. Find the domain of the function and identify any vertical and horizontal asympototes.
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
5 points
QUESTION 8
1. Determine the value that the function f approaches as the magnitude of x increases.
∞
-3
2
-1
0
5 points
QUESTION 9
1. 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
5 points
QUESTION 10
1. 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 asympotote: none
x2; Vertical asympotote: none
5 points
QUESTION 11
1. Determine the value that the function f approaches as the magnitude of x increases.
3
-3
4
-4
-3.67
5 points
QUESTION 12
1. 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.
5 points
QUESTION 13
1. 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
5 points
QUESTION 14
1. 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
5 points
QUESTION 15
1. 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
5 points
QUESTION 16
1. 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)
5 points
QUESTION 17
1. 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)
5 points
QUESTION 18
1. Select the correct graph of the function
5 points
QUESTION 19
1. Select the graph of the rational function. (Plotted additional solution points as needed.)
5 points
QUESTION 20
1. 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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