First of all, it is not technically correct to talk about the image of a function. Strictly speaking we are talking about the image of a set under that fuction.
For example, the function [itex]f(x)= x^2[/itex] maps any number in the interval [-1, 1] into the interval [0, 1]. We say the "the image of [-1, 1] under the function [itex]f(x)= x^2[/itex] is [0, 1]. Sometimes you will see "the image of the function" to mean the image of the entire domain of the function f, under f. The "standard domain" for [itex]f(x)= x^2[/itex] is all real numbers which is mapped into the set of non-negative numbers, [itex][0, \infty)[/itex] so we might say that the "image" of a function is its range but I do not consider that to be correct terminology. It is the image of the set, not the function.