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