Math 112   Final Exam 8 pts each       May 9, 2002

 

Solve for x.

1.    

 

 

2.    mx - ay = 2x + c(x - 1)

 

 

3.  | 4x + 2 | < 4

 

4.      x2 -4x = 6

 

5. 

 

6.  x1/2     -3x1/4 + 2  = 0


7.  If a and b are negative numbers and b/a is greater than 1, then is a-b positive or negative?

 

8.  Find the equation of the circle .

 

9.  Find the center and radius of the circle whose equation is x2 + y2 - 10x - 4y = 7

 

 

10.  Write the equation for the line that has:

 

a.   slope 2 and y intercept 5

 

b.   slope -1/2 and passes thru the point (-2, 5)

 

c.  has zero slope and passes thru the point (5, -6).

 

d.  Passes thru the points (-2, -3) and  ( -1, 5)

 

 

11.  Give the domain and range for each of the following.

a.

 

b. 

c. 

 

d.

 


12.  Find the domain of:

 

a.  y = x2 - 3x + 2

 

b.  y =

 

c.  y =

 

 

13.  If g(t) = 4 - 3t and G(u) = u - u2, find

 

 

 

14.  Find the domain and range and state whether or not the relationship represents a function. :

 

{ (1,2), (3,2), (-2,4)}

 

15. Graph, find  axis of symmetry, vertex, and max or min value of the function   f(x) =  -2x2 - 8x +4  .

 

 

16.     Sketch the graph of : 

 

  

 

 

17.   a.   Write the equation of a function that is

            not 1-1

 

b.  .  Write the equation of a function that is 1 -1.

 

18. Graph the inverse of this function on the same xy plane.

19.   Find f-1(x) for

 

 

 20.  Divide by long division.

(x3 - x + 3 ) Ö (x - 3)

 

 

21.  Divide by synthetic division.

(2x2 - 3x + 1) Ö (x - 2)

 

22.  Find the equation of the polynomial P(x) that has zeros 3 (multiplicity 2), and -1 (multiplicity 3), and graph.

 

 

23.  Find the equation of the function in the graph.

 

 

24.  Find the x intercepts , y intercept, vertical asymptotes, and horizontal asymptote for