Can a function be even AND odd?

Question

Can a function be both even and odd? And, how can a linear function be odd? Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts?

Answer 1

1.) Yes. f(x) = 0 is even and odd, because f(-x) = f(x), and f(-x) = -f(x).

2.) A linear function may be odd if it's symmetric with the origin, for example: f(x) = x is odd, because f(-x) = -f(x). -x = -x.

3.) Yes. A polynomial of the form (x - a)^2 + (y - b)^2 = r^2 forms a circle, so you could define a circle so that it does not have an x or y intercept. Example:
(x - 5)^2 + (y - 5)^2 = 4 is a circle with a center at 5,5 and a radius of 2. It's polynomial form would be: x^2 + y^2 - 10x - 10y - 46 = 0