Why is it impossible for a function to have fewer values in its domain than in its range?

It is impossible for functions to have fewer values in its domain than its range because from the definition of a function,

A function is an equation wherein for every independent variable there is one and only corresponding dependent variable.

For example, for x = 1 the value of y = 0. It is also possible for x = 2 to have a value of y = 0. However, it is impossible for x = 1 to have a value of y = 0 and 1.