Give an example of an even function and explain algebraically why it is even

Even Function. A function with a graph that is symmetric with respect to the y-axis. A function is even if and only if f(–x) = f(x). See also. Odd function.
They got called "even" functions because the functions x2, x4, x6, x8, etc behave like that, but there are other functions that behave like that too, such as cos(x):