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

May 18, 2015

(-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 $f : D \to \mathbb{Z}$ by the explicit mapping:
$f \left(- 4\right) = 1$
$f \left(- 2\right) = - 2$
$f \left(1\right) = - 9$

The range $R$ of the function $f$ is the set {-9, -2, 1} of values in $\mathbb{Z}$ which $f \left(x\right)$ takes for $x$ in $D$.

May 18, 2015

Yes, the set $\left\{\begin{matrix}- 4 & 1 \\ 1 & - 8 \\ - 2 & - 2\end{matrix}\right\}$ 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.