Math 112       Final    16 points each        Dec 11, 2000

 

 


1.  Find the domain and range of

 

2.  Graph the function:

 

3.  Find the domain and range of the function whose graph is :

 

 

4.  In the function f(x) = -4(x-2)2 + 3 :

a.  Which number controls horizontal shift?

b.  Which number controls vertical shift?

c.  Which number controls whether the parabola opens up or down?

 

 

5a.  Write an equation of the parabola whose vertex is located at (-2,3) and points upward.

 

b.  f(x) = ax2 + 5  has x intercept 10.  Find a.

 

6.  a.  Use long division to find the quotient and remainder of

 

b.  Use synthetic division to find quotient and remainder of

 

7.  a.  Simplify:   

b.  Rationalize the denominator

 

8.  Write the equation for a line:

a.  with slope 0 and y intercept -2 .

b.   Thru  ( -1, 3) with undefined slope.

c.  Thru (2,3) and (-1, 4)

 

9.  Graph :

 

a.  y = (1/4)-x

 

b.  y = log2 x

 

10.  Use the laws of logs to:

 

a.  Expand

 

b.  contract as much as possible  log2 28 + log2 12 - log2 84

 

11.  solve for x:  log2(x+1) +  log2 (x - 1)  = 3

 

12.  Solve for x:  32x + 5  = 4 x + 1