Show that affine functions are both concave and convex

[retspool]

Homework Statement

In my textbook, the author briefly makes a statement that affine functions are both concave and convex, how is that true? and how can it be proven?

Homework Equations

The Attempt at a Solution

 

[asap9993]

Isn't an affine function a line?
Lines don't have any concavity.

 

[retspool]

This is exactly how the problem goes
let f(x) be a function in Rn.
prove that f(x) is both concave and convex if f(x) = cTx for some vector c

I thought that the function was a affine function, but i can't prove it