is there any other method of finding onto into functions other than making graphs

A function is said to be onto if there exist an x for every y.

Hence to prove a function to be onto just solve the function for an x

Eg: f(x) = 3x + 5

Let f(x) = y = 3x + 5

x= (y-5)/3

Hence there exist a x for every y

And hence the function is onto