Find the maximum or minimum function value in the interval

Question

1. Find the vertical asymptote(s) of F(x) = (3x - 1) / (x² - 3x)

A.x = 1/3
B.x = 3
C.x = 0 and x = 3
D.None

2. Find the horizontal asymptote of F(x) = (5x² + 1) / (x² + 2x + 1)

A. y = 5
B. y = -1
C. None
D. y = 0

3. Find the horizontal asymptote of F(x) = 3x / (x² - 4)

A. y = 2
B. None
C. y = 0
D. y = 3

4. Graph F(x) = x / (x + 3)

A. I
B. II
C. III
D. IV

5. Graph F(x) = 2 / (x² - 9)

A. I
B. II
C. III
D. IV

6. Graph F(x) = (x + 1) / (x² - x - 6)

A. I
B. II
C. III
D. IV

7. On the graph for: y = (2x² - 5x + 3) / (x² - x - 2), 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) = 5000p / (100 - 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) = (31000t² + 580) / (2t² + 5t + 24), 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)=(2x - 1) / 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) = (4x² - 1) / (x² -16)

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.

12. Given: F(x) = x / (x² - 9)

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?