**Practice Exam 1 -- Answers and Some Solutions**

**1. **
Since a power of a power corresponds to the product of exponents, and product of powers to the sum of exponents we obtain:

=

Hence, the answer is
**(C)**
.

**2.**
We multiply numerator and denominator by
, take into account that
and obtain
. We can cancel one y, and obtain
**(B)**
.

**3. The expression can't be simplified. The numerator and the denominator have no common factors! (D)**

**4.**
**(C)**

**5.**
By distributivity
. That gives
**(A).**

**6. **
We can factor out x and expand
.
**(B).**

**7.**
By expanding
and writing the denominator as
we obtain
**(B). **

**8.**
The lowest common denominator is
. Hence

We regroup terms in the numerator and obtain
**(A)**
.

**9.**
A quotient is 0 if and only if the numerator is 0. Hence, the equation is equivalent to
, which has two solutions x=4 and x=-4. At x=1 the expression is undefined. Thus x=1 is not a solution. The answer is
**(C)**
.

**10.**
means by the geometric interpretation of the absolute value that the distance of x from 2 is less than 2. Hence, x must be between 0 and 4.

**11.**
By simple algebra we obtain the solution
.

**12. (B)**

**13. **
** **

**14.**
, so f(10)=-99=f(-10).
. Expanding the square and simplifying, we obtain
.

**15. **
Increasing in (
) and (
), decreasing in (-1,1). Never constant.

**16. **
Relative minimum at
, maximum at
.

**17. **
The function is odd as clearly
, or, in other words, the graph is symmetric with respect to the origin.

**18. **
, f(2) we estimate to be about 2. We estimate the points where f(x)=0 as x=-1.8,0,1.8.

**19.**
No. It does not pass the vertical line test.

**20.**
The function is
. That is,
. The graphs of g(x) and h(x) look as follows:

**21. **
Solving for y gives us
. Hence, the slope is
, y-intercept 3.

**22.**
The slope of a perpendicular line is the negative reciprocal of the slope of the original line. In our case,
. Since the line passes through (0,0), the y intercept is 0. Hence, the equation is
.

**23.**
If you put all the parentheses correctly, you obtained the correct answer 32.0478....

**24. **
The function is even as f(-x)=f(x). f(2)=f(-2)=12.

**25.**
y=0.15625x

**26. **
12

**27. **

**28. (a) **
1+3i
**(b) **
1+2i