2.3 Properties of Functions A heart is not judged by how much you love, but by how much you are loved by others. -Wizard of Oz

Even and Odd Functions A function is even if for every number x in its domain, the number -x is also in its domain and A function is odd if for every number x in its domain, the number -x is also in its domain and Symmetry about the y-axis Symmetry about the origin

Even and Odd Functions State whether each function is even, odd, or neither. Then state any symmetry.

Even and Odd Functions Determine whether the following functions are even, odd, or neither. Then state any symmetry. 1) 2) 3) 4)

Decreasing, Increasing, and Constant (OH MY!) Determine the intervals when the following function is decreasing, increasing, or constant.

Local Minima and Maxima Could be more than one of each on a graph!

Local Minima and Maxima Locate any local minima and maxima in the following graph.

Graphs Use the graph of the following function identify any local maxima or minima. Find all intervals where the function is increasing, decreasing and constant (0, -3) (2, 3) (4, 0) (10, -3) (1, 0) x y (7, -3) a)Local Maxima (point) b)Local Minima (point) c)Increasing (domain interval) d)Decreasing (domain interval e) Constant (domain interval)

Average Rate of Change Given a function y = f (x), the average rate of change of f from a to b is defined as Average rate of change Secant Line ab f (b) – f (a) b – a

Average Rate of Change Given a function y = f (x), the average rate of change of f from a to b is defined as Average rate of change Secant Line – 3 16 – 5

Average Rate of Change Find the average rate of change of the function below from -2 to 6. Then find the equation of the secant line connecting the points. Average rate of change

2.3 Properties of Functions A heart is not judged by how much you love, but by how much you are loved by others. -Wizard of Oz Homework: #19 p.89 #11-43 odd, odd