**Practice Exam 2**

Exam 2 covers sections R6, 2.4, 2.7, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3. The actual Exam 2 will be shorter than the practice test. The format of Exam 2 will be similar to that of the practice test.

**Part I**
** **
--** No calculators allowed.**

**Some of 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 Exam I. **
**In all problems, your explanations should consist of complete sentences and correct mathematical formulas.**

**1. **
Simplify

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

**2. **
Simplify.

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

**3. **
Simplify

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

**4. **
Write as one quotient and simplify

**(A) **
**(B) **
**(C) **
**(D) **
Can't be done

**5. **
Assume c >0, d> 0. Simplify

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

**6. **
Assume a>0, b>0. Simplify

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

**7. **
Find the following logarithms, if defined. If not, write "undefined".

(a) =

(b) =

(c) =

(d) =

(e) =

(f) =

**8. **
Simplify

(a) =

(b) =

(c) =

**9. **
Without using your grapher, find all vertical and horizontal asymptotes of
.

**10. **
Does the function
have any vertical asymptotes? Explain!

**11. **
Solve the following inequalities. Represent your solutions graphically on the number line.

(a)

(b)

**Part II**
** -- You can use your calculators if you wish.**
**In all problems, your explanations should consist of complete sentences and correct mathematical formulas.**

**12. **
Find the center, the radius, and the equation in the standard form for the circle

.

HINT: Complete the square in x terms and in y terms.

**13. **
By completing the square, find the vertex of the parabola
.

**14. **
Solve the following equation by completing the square, without the quadratic formula:

.

**15. **
Solve the following inequalities:

(a) (b)

**16. **
Factor completely into polynomials of degree one

**17. **
Is the following function one to one?
** Explain!**

**18.**
Is the following function one to one?
** **
**Explain!**

**19. **
Find a rational function that has y=2 as its horizontal asymptote and x=3 as a vertical asymptote.

**20. **
For the function

find all horizontal and vertical asymptotes. Graph the function.

**21. **
Using a grapher, estimate all zeros of the polynomial

.

**22.**
Let
,
. Divide P(x) by d(x) using
**long division**
. Write P(x) in terms of the divisor, the quotient, and the remainder.

**23. **
For the following functions
* f(x), *
find the inverse
*(x)*
if exists. If the inverse exists, graph both functions in one coordinate system.

(a) , domain: all x. (b) , domain: all x (c) , domain:

**24. **
Find the inverse function. You don't have to graph anything.

(a) (b)

**25. **
Let
,
. Find the composite functions f(g(x)) and g(f(x)). You don't have to simplify anything.

**26. **
For each function h(x) below, find at least two ways of representing h(x) as a composition h(x)=f(g(x)):

(a) (b)

**27. **
Graph
and
in one coordinate system. How are the two graphs related?

**28. **
Using your calculator, find

** **
(a)
=

(b) =

(c) =

** **
(d)
=

In each of (a)-(d), explain your method.