Practice Exam 1

Exam 1 covers through section 2.2, including 2.2. 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 have to show your work, no credit will be given without work. Partial credit is possible.

1. Simplify

(A) (B) (C) (D)

2. Simplify

(A) (B) (C) (D)

3. Simplify

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

4. Simplify

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

5. The expression

is equal to:

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

6. Factor as far as you can the expression

(A) (B) (C) Can't be factored (D)

7. Simplify as far as possible

(A) (B) (C) (D) None of the above

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

(A) (B) (C) (D)

9. Solve for x

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

10. What is the set of all x for which

?

11. Solve for x

12. Simplify

(A) (B) (C) (D) None of the above

Part II -- YOU CAN USE YOUR CALCULATORS IN THIS PART

13. What is the domain of the function

?

14. For , find and simplify if possible

(a) (b) (c)

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

(a) increasing (b) decreasing (c) constant

16. The function in the graph above has

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

17. Is the function in the graph above

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

18. Given the graph of the function above, find, or estimate, the values:

(a) (b) (c) At what points x we have f(x)=0?

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

20. 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.

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

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

23. Use your calculator to calculate the value of

24. Consider .

(a) Is f(x) odd, even or neither? (b) Calculate and .

25. Suppose varies directly as and when . Find an equation relating to .

26. If and , then = ?

27. The points (-3,-1) are and (9,4) are endpoints of the diameter of a circle. Find the equation of the circle.

28. Write in the form

(a) (b) 1+