How do even and odd functions relate to even and odd numbers? How do the notions of oddness and evenness apply to both functions and numbers?
If Even and Odd functions share nothing in common with Even and Odd numbers, then why were Even and Odd adopted for functions? Why not use other adjectives?

James Stewart, Calculus 7th ed. 2011. This isn't the Early Transcendentals version.

For an even function $f(-x)=f(x).$  Now you know that $(-x)^n=x^n$ if $n$ is even.
For an odd function $g(-x)=-g(x)$. Now you also know that $(-x)^n=-x^n$  if $n$ is odd.
