You should KNOW

1. What the graphs of the basic power functions *f(x) = axn *look like for different values of n e.g. n = 2, 3, ..., -1, -2, 1/2, -1/2, etc.

2. What the graphs of the absolute value function f(x) = |x| looks like, and how to graph "piecewise functions."

3. How to recognize functions that are *increasing, decreasing, or constant* on given intervals.

4. How the graph of y=f(x) is affected by adding/ a constant to x, or adding a constant to f(x), e.g. how the graph of y = f(x - 3) + 2 is related to the graph of y = f(x).

5. How the graph of y = f(x) is affected by multiplying f(x) by a constant, e.g. how the graph of y = -3f(x) is related to the graph of y = f(x).

6. The meanings of "odd function" and "even functions" and how to apply algebraic tests related to these concepts.

You should be ABLE TO

1. Recognize graphs of power functions, the absolute value function, and piecewise functions, and their various shifts and stretches, and be able to create such graphs yourself, with and __without__ a graphing calculator.

2. Describe the effect of shifts and vertical stretches of graphs on the algebraic expressions for the corresponding functions.

3. Determine symmetries of graphs of functions from their algebraic forms.