Question

The value y is a function of x if for each element x in the domain, there is/are how many value(s) of y in the range?

Answer 1

In a function f(x):

set of all the values that x can take is called the domain of the function.

Set of all the values that f(x) (or y) can take is called the range of the function.

Range can have either finite or infinite number of values depending on the function its domain.

For example, f(x) = x^2
can have infinite number of values in range.

whereas :
f(x) = [x] , 0<x<10
where [x] is the greatest integer function,

has finite number of values in its range.