1. College Algebra 2.4 Properties of Functions Objectives: 1. Determine even or odd functions 2. Determine behavior of a function. 3. Find local min and max. 4. Find average rate of change of a function.

2. Even or Odd  If a function is even then for every x,  f(x) = f(-x)  Even functions are symmetric with the y=axis.  If a function is odd, then for every x,  f(-x)=-f(x)  Odd function are symmetric to the origin.

3. Example  Determine if the following graphs are even, odd, or neither.

4. Example 2  Determine if the following equations are even, odd, or neither.

5. Example 3  Determine the intervals in which the function is increasing, decreasing, or constant.

6. Local Maxima and Local Minima  Wherever a function changes from increasing to decreasing, there is a local maxima.  Wherever a function changes from decreasing to increasing, there is a local minima.  These can be found visually and by using the max and min tools on the graphing calculator.

7. Average Rate of Change  Use the slope formula between any two points on the curve.  We are limited in algebra to finding the average rate of change.  We are unable to find the change occurring at any one time.  Calculus is the field of mathematics that allows us to find instantaneous rates of change on any curve.

8. Example 4  Given f(x) = 2x 2 + 1, find the average rate of change from  A. 2 to 3 B. 2 to 5

9. Practice  Page 236: 1- 39 odds, 53, 55, 65