**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

**Be sure to explain all your answers! No credit without explanations.**

**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+