Math 113 - 0203     Exam 2     Monday 8-12-2002    Name__________________________

Do all problems in the space provided.  Mark your final answers clearly and make sure answers are simplified.  Give exact answers to all questions; do not use decimal approximations.  You must show appropriate work to receive credit for an answer.  Calculators are not allowed.

For problems 1 - 6, sketch the graph of the following functions.  In particular, your graph should accurately show the position of x- and y- intercepts (if any), horizontal and vertical asymptotes (if any) and the vertex (if applicable).

1.  (5 pts)   h(x) = ln (x -2)

2.  (8 pts)   f(x) = -2(x^2) + 4x + 6

3.  (10 pts)   g(x) = \(TraditionalForm\`\(\(-2\) \(\(x\^2\)(x\  - \ 6)\) \((x\  + \ 3)\)\)\/\(\((x\  - \ 1)\) \(\((x\  - \ 4)\)\^2\) \((x\  + \ 4)\)\)\)

4.  (10 pts)   j(x) = - (x^2)(((x  +  2))^3)(x - 4)

5.  (7 pts)   k(x) = ((x  -  9)/(x  +  3))

6.  (10 pts)   m(x) = \(TraditionalForm\`\(6 \((x\  + \ 1)\)\)\/\(\((x\  - 2)\) \((x\  + \ 3)\)\)\)

7.  (6 pts) Find the inverse of the function f(x) = ((2  x  -  1)/(x  +  2)) (you may assume that the inverse exists).

8.  (9 pts) For each of the following functions, tell whether they are 1-1 or not.  Give a reason for your answer.
	a. 						b.  f(x) = 4 (x^2) - 5 x + 3		c. f(x) = 5(x^8) - 4 (x^2)

9.  Solve for x or state that no solutions exist.  Give only exact answers (no decimal approximations):
	a.  (2 pts)   (e^(x -  3)) = 22
	
	
	
	b.  (6 pts)   log x + log (x - 2) = 1

10.	a.  (4 pts) Rewrite in terms of natural logs:  (Subscript[log, 7]) 33

	b.  (3 pts) Write in logarithmic form:  (4^v) = 3.8
	
	c.  (6 pts) Write the following as a sum or difference of logarithms.  Your answer should include no exponents
		or logarithms of products or quotients:  ln ((z^5)((x^2) - 16))

d.  (4 pts) Suppose a = log x and b = log y.  Rewrite the expression log (((100  (x^5))/(Sqrt[y]))) in terms of a and b (your
		answer should not contain any x's or y's).

11.  (4 pts) Suppose you invest $2000 at 5% annual interest, compounded continuously.  How much money will you
	have after 3 years?  Leave your answer in terms of e.

12.  (6 pts) Suppose R(x) is a rational function such that R(x) = ((P(x))/(Q(x))) where P(x) and Q(x) are polynomials.  Suppose
	this is the graph of R(x):








	a.  One of the graphs A,B,C,D,E,F is the graph of P(x).  Which one is it, and how do you know?





	b.  One of the graphs A,B,C,D,E,F is the graph of Q(x).  Which one is it, and how do you know?

In the space below, please copy the following and sign your name:
	I pledge on my honor that I have neither given nor received unauthorized aid on this exam.