Even Functions: An even function has the property that opposite inputs result in the same output. Algebraically, we say that \(f(x)\) is an even function if the following is true:

\[ f(-x) = f(x) \]

Odd Functions: An odd function has the property that opposite inputs result in opposite outputs. Algebraically, we say that \(g(x)\) is an odd function if the following is true:

\[ g(-x) = -g(x) \]