f(x) = (x - 3)2, with domain [3, ∞)

What is the range of function f?

Knowing that the function is linear, we can safely evaluate the function at the two extremes of the domain to obtain the range.

f(x)=2(x-3)
f(3)=2(3-3)=0
f(∞)=2(∞-3)=∞

Therefore the range of f(x) is
[0,∞)