Practice Exam 1

Exam 1 covers sections R1-R8, 1.1, 1.2, 1.3, and 1.7. The actual Exam 1 will be shorter than the practice test. The format of Exam 1 will be similar to that of the practice test.

Part I -- No calculators allowed. This is in case you have one of those powerful calculators TI 89 or TI 92 that can do symbolic algebra.

The problems below seem like multiple-choice problems, but indeed they are not. You will have to show your work, no credit will be given without work. Partial credit is possible, similarly as on Quiz I.

1. Simplify

(A) (B) (C)

2. Simplify

(A) (B) (C)

3. Simplify

(A) (B) (C) Can't be simplified

4. Simplify

(A) Can't be simplified. (B) (C)

5. The expression

is equal to:

(A) (B) (C) Neither (A) nor (B).

6. Factor completely the expression

(A) (B) (C)

7. Simplify as far as possible

(A) (B) (C)

8. Simplify.

(A) (B) (C)

9. Simplify

(A) (B) (C)

10. Find the lowest common denominator, write as one quotient, simplify

(A) (B) (C)

11. Solve for x

(A) x = 1, x = 4 (B) x = 1, x = 4, x = -4 (C) x = 4 , x =-4

12. What is the set of all x for which

?

13. Solve for x

14. Write as one quotient and simplify

(A) (B) (C)

15. Assume c >0, d> 0. Simplify

(A) (B) (C)

Part II -- You can use your calculators if you wish.

16. What is the domain of the function

?

17. For , find and simplify if possible

(a) (b) (c)

18. Determine intervals on which the function given by the graph below is

(a) increasing (b) decreasing

19. The function in the graph above has

(a) A relative maximum at x =______ (b) A relative minimum at x = ______

20. Is the function in the graph above

(a) even (b) odd (c) neither

21. Is the graph given below the graph of some function? Explain.

22. Below you see the graph of a function . Write a formula and sketch the graph of the function whose graph is obtained from the graph y=g(x) by a vertical stretch by the factor 2 and horizontal shift by 2 units to the right.

23. Find the slope and the y-intercept of the line given by the equation

24. Find an equation of the line that passes through (0,0) and is perpendicular to the line .

25. Use your calculator to calculate the value of

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