# Functions, Asymptotes, Intercepts, Maxima and Minima

Please see the attached file for the fully formatted problems.

1. Find the vertical asymptote(s) of F(x) =

A.

x = 1/3

B.

x = 3

C.

x = 0 and x = 3

D.

None

2. Find the horizontal asymptote of F(x) =

A.

y = 5

B.

y = -1

C.

None

D.

y = 0

3. Find the horizontal asymptote of F(x) =

A.

y = 2

B.

None

C.

y = 0

D.

y = 3

4. Graph F(x) =

A.

I

B.

II

C.

III

D.

IV

5. Graph F(x) =

A.

I

B.

II

C.

III

D.

IV

6. Graph F(x) =

A.

I

B.

II

C.

III

D.

IV

7. On the graph for: y = , what happens as x approaches negative infinity?

A.

y goes to infinity

B.

y goes to negative infinity

C.

y approaches 2 (gets closer and closer but never reaches it)

D.

y approaches -1 (gets closer and closer but never reaches it)

8. The cost C in dollars to remove p% of the pollution in a small pond near a factory is given by C(p) = , 0 p < 100. Find the cost of removing 75% of the pollution.

A.

$38

B.

$5068

C.

$15,000

D.

$200

9. A factory finds that the number of items it can produce per week after t weeks of production is approximated by C(t) = , t 0. Theoretically, what is the most the factory could produce in a single week, according to this equation.

A.

14,500

B.

15,500

C.

16,500

D.

31,000

10. The profit, in thousands of dollars, of manufacturing x items is projected by: P(x)= , x>0 According to this projection the profit will never exceed ______.

A.

$2000

B.

$10,000

C.

$20,000

D.

there is no limit

11. Given: F(x) =

a. Find the x-intercept(s).

b. Find the y-intercept(s).

c. Find the vertical asymptote(s) (write as an equation of a line).

d. Find the horizontal asymptote(s) (write as an equation of a line).

e. For x>4, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.

f. Find the maximum or minimum function value in the interval -4 x 4, and state whether it is a maximum or minimum value for that interval.

g. Describe what happens on the graph when x approaches infinity.

Answer

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12. Given: F(x) =

a. Find the x-intercept(s).

b. Find the y-intercept(s).

c. Find the vertical asymptote(s) (write as an equation of a line).

d. Find the horizontal asymptote(s) (write as an equation of a line).

e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.

f. Is the function increasing or decreasing in the interval -3 x 3?

g. As x approaches 3 from the left, what happens to the function values?

h. As x approaches 3 from the right, what happens to the function values?