Is $f(x,y) = x - y$ convex?

Question

I know that linear functions are both convex and concave, except the negative summation does not uphold the convexity. Due to this fact, is it safe to assume that $f(x,y) = x-y$ is not convex?

Answer 1

Every real-valued linear transformation is convex but not strictly convex, since if $f$ is linear, then $f(a+b)=f(a)+f(b)$.