Question

suppose f(x) = x2, how does the range of g(x) = f(x) + k compare to the range of f(x)? Where k is any constant value.

Answer 1

First: Please use the symbol " ^ " to indicate exponentiation. Your f(x) should be x^2, not x2. "x^2" reads "the square of x."

Let y equal g(x) = f(x) + k: y = g(x) = f(x) + k. See that "k" is a y value?
If k=1, we merely translate the graph of f(x)=x^2 UP one scale division to obtain the graph of g(x) = f(x) + 1.

So, how does the range of g(x) compare to the range of f(x)?