What is a nonlinear functions?

Answer 1

it's linear if for any x,y,k values: f(k*x + (1-k)*y) = k*f(x) + (1-k)*f(y)

or, an equivalent condition:

it's linear if for any k value: f(k) = k*f(1) + (1-k)*f(0) = f(0) + k*(f(1)-f(0))

examples:

f(x) = 7, x, 2x, 11-3x

non-linear in any other case. examples:

f(x)=x^2, sin(x), 1/x, ln x

Answer 2

A non linear function is any function that can't be graphed as a straight line. Basically, it is every single function except one that can be represented by the function y = m*x + b.

Answer 3

A function which doesn't form a line. It could form a parabola. These can be achieved from quadratic functions, cubic functions, etc.