How do you determine algebraically if an equation is odd eve

How do you determine algebraically if an equation is odd, even, or neither?

Solution

We can use following Test to determine if a function y=f(x) is even, odd or neither:
Replace x with -x and compare the result to f(x).
If f(-x) = f(x), the function is even. If f(-x) = - f(x), the function is odd.

Even Functions

A function is \"even\" when:

f(x) = f(x) for all x

In other words there is symmetry about the y-axis

The curve f(x) = x2+1

The \"even\" functions because the functions x2, x4, x6, x8, etc look like this. The mirroring about the axis is a hallmark of even functions.

Odd   Functions

A function is \"odd\" when:

f(x) = f(x) for all x. And we get origin symmetry.

If f(-x) f(x) and f(-x) -f(x), the function is neither even nor odd.