Question

If you are given a set of points on a graph (0,0), (1,4), (2,1), (3,3), (4,5), how do you determine the domain of the function?

Answer 1

The domain contains the set `{0,1,2,3,4}`

Explanation:

The domain of a function is the set of values which the function can operate on. In this case, that means the set of possible `x` values. Without knowing anything about the function beyond the given points, we cannot say with certainty which `x` values are valid except for the ones already shown, that is, the values `0, 1, 2, 3,` and `4`.

For example, the function could be defined as a function `f` such that
`f(0) = 0`
`f(1) = 4`
`f(2) = 1`
`f(3) = 3`
`f(4) = 5`

As `f(x)` is only defined for `x in {0,1,2,3,4,5}`, those would make up its entire domain.

Alternatively, we could have a function like

`g(x) = −17/24x^4+25/4x^3−415/24x^2+63/4x`

At the given points, `g(x)` is identical to `f(x)`, however `g(x)` is defined for all real numbers, and thus the domain for `g(x)` is `RR`.

As we can see, there is no way to know the exact domain without knowing more about the function. We can only say that it contains the given values.