Question

Is (-4,1), (1,-8), (-2,-2) a function?

Answer 1

(-4,1), (1, -9) and (-2,-2) are just three distinct points.

They are not a function as such, but they could be used to define a function.

Let `D` be the set {-4, -2, 1}. This is the domain of the function.

Define `f:D->ZZ` by the explicit mapping:
`f(-4)=1`
`f(-2)=-2`
`f(1)=-9`

The range `R` of the function `f` is the set {-9, -2, 1} of values in `ZZ` which `f(x)` takes for `x` in `D`.

Answer 2

Yes, the set `{(-4,1), (1,-8), (-2,-2)}` is a function.

A function is a set of ordered pairs in which no two pairs have the same first element and different second elements.

This definition, in a way, tells us how a collection of ordered pairs call fail to be a function.

The set you asked about has no two pairs with equal first and different second elements. So it is a function.