math_6.docx

QUESTION 1

Find the domain of the function https://content.grantham.edu/at/MA105/exams/w6_1.jpg

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

Find the domain of the function https://content.grantham.edu/at/MA105/exams/w6_2.jpg

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

Determine the domains of f and g.

https://content.grantham.edu/at/MA105/exams/w6_3.jpg

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

Find the domain of https://content.grantham.edu/at/MA105/exams/w6_4.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_5.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_6.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_7.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_8.jpg

-3

2

-1

0

5 points   

QUESTION 9

Simplify f and find any vertical asymptotes of f.

https://content.grantham.edu/at/MA105/exams/w6_9.jpg

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

Simplify f and find any vertical asymptotes of f.

https://content.grantham.edu/at/MA105/exams/w6_10.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_11.jpg

3

-3

4

-4

-3.67

5 points   

QUESTION 12

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

https://content.grantham.edu/at/MA105/exams/w6_12.jpg

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

Determine the equations of any horizontal and vertical asymptotes of

https://content.grantham.edu/at/MA105/exams/w6_13.jpg

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

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

https://content.grantham.edu/at/MA105/exams/w6_14.jpg

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

Simplify f and find any vertical asymptotes of f.

https://content.grantham.edu/at/MA105/exams/w6_15.jpg

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

Identify all intercepts of the function.

https://content.grantham.edu/at/MA105/exams/w6_16.jpg

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

Identify all intercepts of the following function:

https://content.grantham.edu/at/MA105/exams/w6_17.jpg

x-intercepts: (±3,0)

no intercepts

x-intercepts: (-3,0)

x-intercepts: (0,0)

x-intercepts: (3,0)

5 points   

QUESTION 18

Select the correct graph of the function

https://content.grantham.edu/at/MA105/exams/w6_18.jpg

https://content.grantham.edu/at/MA105/exams/w6_18_a.jpg

https://content.grantham.edu/at/MA105/exams/w6_18_b.jpg

https://content.grantham.edu/at/MA105/exams/w6_18_c.jpg

https://content.grantham.edu/at/MA105/exams/w6_18_d.jpg

https://content.grantham.edu/at/MA105/exams/w6_18_e.jpg

5 points   

QUESTION 19

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

https://content.grantham.edu/at/MA105/exams/w6_19.jpg

https://content.grantham.edu/at/MA105/exams/w6_19_a.jpg

https://content.grantham.edu/at/MA105/exams/w6_19_b.jpg

https://content.grantham.edu/at/MA105/exams/w6_19_c.jpg

https://content.grantham.edu/at/MA105/exams/w6_19_d.jpg

https://content.grantham.edu/at/MA105/exams/w6_19_e.jpg

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

https://content.grantham.edu/at/MA105/exams/w6_20.jpg

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

No. The function is undefined at P = 100.

Yes