I've been either a student or an instructor in Precalculus or Calculus 1 at about 6 institutions now, and teaching the definition of even functions (where $f(-x) = f(x)$) and odd functions (where $f(-x) = -f(x)$) has been universal.
But why? I don't see how these concepts are so useful that they need to be in the courses that are taught to everyone. I don't see how they lay the stage for understanding calculus.
I mean, seeing how it works graphically is nifty. But it seems like a disproportionate emphasis is placed on these classifications, in every curriculum I've seen.