Week 1 - Use the graph of f given below to find f

Participation Exercises for Week 1  

 

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

The graph of a function f is given. Use the graph to answer the question.

1) Use the graph of f given below to find f( 8).

1) _______

A) 0 B) 12 C) -16 D) 8

 

Find the limit, if it exists.

2) Find: 2) _______

A) - 24 B) 16 C) -8 D) 8

 

Sketch a possible graph of a function that satisfies the given conditions.

3) f(0) = 6; f(x) = 0; f(x) = 0

3) _______

A)

B)

C)

D)

 

Solve the problem.

4) The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of tapes produced. The

average cost per tape, denoted by is found by dividing by x. Find 4) _______

 

A) 6 B) 10 C) 14 D) Does not exist

 

Use the given graph to find the indicated limit.

5)

f(x) 5) _______

 

A) 5 B) ∞ C) -∞ D) 0

 

Find the limit.

6) Determine the limit.

f(x), where f(x) = 6) _______

 

A) -∞ B) -2 C) 5 D) ∞

 

Provide an appropriate response.

7) If the limit at infinity exists, find the limit.

7) _______

 

A) B) 0 C) 1 D) ∞

 

Use -∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes.

8) f(x) = 8) _______

 

A) f(x) = ∞; f(x) = ∞; x = 0 is a vertical asymptote

B) f(x) = ∞; f(x) = -∞; x = -4 is a vertical asymptote

C) No zeros of denominator; no vertical asymptotes

D) f(x) = ∞; f(x) = -∞; x = 4 is a vertical asymptote

 

Provide an appropriate response.

9) Find the horizontal asymptote, if any, of the given function.

f(x) = 9) _______

A) x = 2, x = -2 B) y = 3, y = -4 C) y = 1 D) None

10) Find the horizontal asymptote, if any, of the given function.

f(x) = 10) ______

 

A) y = B) y = C) y = 0 D) None

 

 

Solve the problem.

11) Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by

C(p) = .

Can a company afford to remove 100% of the pollutants? Explain. 11) ______

A) Yes, the cost of removing p% of the pollutants is $ 40,000, which is certainly affordable.

B) No, the cost of removing p% of the pollutants is $ 400, which is a prohibitive amount of money.

C) Yes, the cost of removing p% of the pollutants is $ 400, which is certainly affordable.

D) No, the cost of removing p% of the pollutants increases without bound as p approaches 100.

 

Sketch a possible graph of a function that satisfies the given conditions.

12) f(-1) = -7 ; f(x) = -2; f(x) = -7

12) ______

A)

B)

C)

D)

 

The graph of y = f(x) is shown. Use the graph to answer the question.

13) Is f continuous at x = 2?

13) ______

A) No B) Yes

 

Provide an appropriate response.

14) Use a graphing utility to approximate the partition numbers of the function to four decimal places:

14) ______

A) (-∞, -2.4976)

B) (-∞, -2.4976) ∪ (-2.4976, -0.7203)

C) (-∞, -2.4976) ∪ (0.1832 , 3.0347)

D) (-∞, -2.4976) ∪ (-2.4976, -0.7203) ∪ (-0.7203, 0.1832 ) ∪ (0.1832 , 3.0347)

 

15) Use a graphing utility to find the discontinuities of the given rational function.

g(x) = 15) ______

A) 1 B) 3

C) -1 D) Continuous at all values of x

 

16) Use a graphing utility to find the discontinuities of the given rational function.

f(x) = 16) ______

 

A) 3 B) 1

C) -1 D) Continuous at all values of x

 

17) Use a sign chart to solve the inequality. Express answers in interval notation.

+ 6 < 2x 17) ______

A) {2} B) ∅ C) (-∞, -2) D) (2 , ∞)