DEFINITION. A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin.

How do you know if a function is even or odd?

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

What is an odd function example?

The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x). Some examples of odd functions are trigonometric sine function, tangent function, cosecant function, etc.