Every function is surjective with respect to its image

up:: Image of Function

Given a function $f:X\to Y$, and noting that $f(X)\subset Y$, one can see that all points of $X$ are restricted to reach only the image of $f$ (not any point in $Y\setminus f(X)$).

Thus, every function $f:X\to Y$ can be seen as a Surjective Function $f:X\to f(X)$ when restricting its reach to its image only.

This is also why Injective functions are bijective with respect to their image.