(Problems are 5 points each, unless multiple parts-- 2 each part)

1. Find the domain and range for .

[Hint: Use a graphing calculator to find the range!]

2. Solve for x (explain or describe your method).

.

3. Graph:

4. Given:

a) b) c)

d) Is this graph continuous? Explain your answer.

5. Given:

a) b) c)

d) Is this graph continuous? Explain your answer.

6. If , find f (g(x)) and g(f(x)).

7. If , find f (x + h) – f(x) and simplify completely.

8. If , find

a) and simplify completely.

b)

9. Find .

10. Find .

11. Given:

a) b) c)

d) Sketch the graph.

In 12–13, find f ¢ (x) using the limit definition of the derivative, .

12. .

13.

14. Find f ¢ (x) for by the "shortcut" method (i.e., the power rule).

15. Find f ¢ (x) for by the "shortcut" method.

16. If , find f ¢ (3)

In 17 – 20, the cost function for a company that produces x units per week is given by C(x) = 420 x + 72000, and the revenue is given by R(x) = -3x² + 1800x.

17. Find an equation for profit P(x).

18. Find the company’s break even points (where profit = 0).

19. Find the company’s marginal revenue and marginal profit functions.

EXTRA CHALLENGE

20. Find the number of units that should be produced in order to maximize profit and the maximum profit.

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