Even and Odd Functions

#Functions #Even #Odd #Algebra #Mathematics
A function y = f(x) is an even function of x if f(-x) = f(x) and an odd function of x if f(-x) = -f(x) for every x in the function’s domain.

Important Points for even functions:
1. The graph of an even function is symmetric about the y-axis.
2. The graph of an even function does not change if we reflect it across the y-axis.

Important Points for odd functions:
1. The graph of an odd function is symmetric about the origin.
2. The graph of an odd function does not change if we rotate it by 180º about the origin.
3. The graph of an odd function always passes through the origin.

Other important points:
1. f(x)=0 is the only real function which is both an even function and an odd function.
2. The sum of two or more even functions is also an even function.
3. The sum of two or more odd functions is also an odd function.

This video explains the concept of even and odd function with the help of examples. It is extremely useful for class 11 and class 12 students.

[michaeldirmeyer]

Thanks GLaDOS this was really helpful.