Math 113 - 0203    Exam 1      Monday 7-29-2002	Name_________________________

Do all problems in the spaces provided.  Mark your final answers clearly and write them in simplified form (in particular, simplify any square roots and compound fractions).  You must show appropriate work in order to receive credit for an answer.  Calculators are not allowed.

1.  Line A has equation 5 x - 3 y = 10.
	a.  (2 pts) Find the slope of line A.
	
	
	
	b.  (4 pts) Find the x- and y- intercepts of line A.
	
	

	
	
	c.  (4 pts) Write the equation of the line through the point (2, -1) which is perpendicular to line A.

2.  	a.  (8 pts) Solve for x or state that no solutions exist:  (x/(x  -  2)) + (3/x) = (4/(x(x  -  2)))

b.  (5 pts) If the equation (x^2) - 6x + k = 0 has exactly 1 solution, what must the value of k be?

3.	a.  (6 pts) Find the symmetry in the graph of the equation y = x((x^2) - 2).  Justify your answer using algebra.

b.  (6 pts) Sketch the graph of the function f(x) = |x| - 5.  Is this function even, odd, or neither?

4.  (8 pts) Find the x- and y- intercept(s) of the graph of the equation y = (x^2) - 2x - 8.

5.	a.  (5 pts) Find the domain of the function s(x) = ((Sqrt[6  -  x])/(x  +  2)).




	b.  (5 pts) If f(x) = (1/x) and g(x) = ((x  -  1)/(x  +  2)), find (g ∘ f)(x).  Remember to simplify your answer so that it does not
		contain a compound fraction.
		
		
		
		
		
		
	c.  (3 pts) Given function H(x) = (((2  x  -  3))^4), find functions f and g such that H = f ∘ g.

6.  (9 pts) Given each of the following graphs or diagrams, tell whether or not they represent a function.  You should give
	some brief justification of your answer.

7.  	(10 pts) For each of the graphs shown, write a function which could have the graph shown:

8.  (6 pts) Draw a graph of a function g(x) in the axes below such that g(x) has all of the following properties:
	(1)  The domain of g is [-5, 3].
	(2)  g is increasing on (0,2) and decreasing everywhere else.
	(3)  f(0) = -2.

9.  (14 pts) The graphs of the functions g and h are shown below.
							a.  (2 pts) What is g(2)?
							
							b.  (3 pts) What is the range of h?  Your answer should be in 
							interval notation.
	
							c.  (3 pts) On what interval or intervals is h decreasing?
	
							d.  (3 pts) For what values of x, if any, does h(x) = 3? 
	
							e.  (3 pts) What is (h ∘ g)(-1)?

10.  (5 pts) One of the graphs A, B, C, or D is the graph of the equation (y^6) - y = 5(x^4) - 3 (x^2) + 2.  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.