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# 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?

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