**Practice Exam 1 -- 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 radical can't be distributed over a sum! (C)**

**4.**
**Can't be simplified! You can't cancel a's! (A)**

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

**6. **
We can factor out x and expand
from the formula
.
**(C).**

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

**8.**
The radical of the radical corresponds to the power (1/2)*(1/2)= 1/4 . We obtain
which gives us
. This easily leads to
**(A)**
.

**9.**
We have
. Since the radical of a product is a product of radicals, and
, we obtain
**(B).**

**10.**
The lowest common denominator is
. Hence

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

**11.**
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)**
.

**12.**
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.

**13.**
By simple algebra we obtain the solution
.

**14. **
We take the common denominator which is
. We obtain
which leads
**(A)**
.

**15. **
Since the radical of a product is a product of radicals, and
,
,
, we obtain
**(B)**
.

**16.**
For the radical to be defined, it must be
. Hence, x must be in the interval [-2,2].

**17.**
, so f(10)=-99=f(-10).
. Expanding the square and simplifying, we obtain
.

**18. **
Increasing in (
) and (
), decreasing in (-1,1).

**19. **
Relative minimum at x=1, maximum at x=-1.

**20. **
The function is odd as clearly
, or, in other words, the graph is symmetric with respect to the origin.

**21.**
No. It does not pass the vertical line test.

**22.**
The function is
. That is,
. The graphs of g(x) and h(x) look as follows:

**23. **
Solving for y gives us
. Hence, the slope is
.

**24.**
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
.

**25.**
If you put all the parentheses correctly, you obtained the correct answer 32.0478....