1.  Give the domain, range, and zeros of each function.

        a. 

        b. 

        c. 

2.  Graph g(x) and find the domain, range and zeros of g.

3.  Determine algebraically whether the graph of x² - xy + y² = 6 has symmetry in:
        a.  the x-axis
        b.  the y-axis
        c.  the origin
        d.  Is it even, odd, or neither?

4.  Given the graph of y = f(x) as shown, sketch the graph of each of the following:

        y = f(x)  Each tic mark on the axes is 1 unit.

       a.  |3 f(2 - x)|                    b.  y = - f(.5|x|) + 2

5.  The water in a cylindrical tank 6 ft in diameter empties through a hole in the bottom.
     Assuming that the water has a depth of 15 ft at time t = 0 and empties at the rate of
     4 ft³/s, express the depth of the water as a function of time.

6.  Rectangle ABCD has two vertices on the semicircle   and two vertices
     on the x-axis.

  Each tic mark is 1 unit.  Ignore the parts of the
                                                      vertical lines outside the circle.

        a.  Express the area of the rectangle as a function of the x-coordinate of A.
        b.  What is the domain of the area function?
        c.  Find the maximum area.

7.  Graph y = ||x - 3| - 2| + 1

8.  Graph y = |x³ - 36x|

9.  Graph y = |x² - 2x - 6|

10.  If f(x) = 2x² - 3  and ,  find

        a.  f(4)
        b.
        c.  f (x + h) - f (x)
                      h
        d.  g(x) - g(14)
                x - 14

11.  On what intervals is h(x) increasing if the graph of h(x) is the following:

Each tic mark is 1 unit.

Answers