How to use PlusMinus properly?

Question

As an easy exercise, I would like to define a function

$$f(x)=\pm x$$

and be able to ListPlot the function for some discrete values.

Here is what I tried

F[x_] := PlusMinus[x];
Table[F[x], {x, 1, 4}]

This gives me output

{\[PlusMinus]1, \[PlusMinus]2, \[PlusMinus]3, \[PlusMinus]4}

This is exactly what I want. But now I want to listplot it using

ListPlot[Table[F[x], {x, 1, 4}]]

But this does not give me output.

So, I guess my question is how to convert the output of PlusMinus[2] which is $\pm2$ to an array $\{-2,2\}$ so that I can do other operations on it.

Answer 1

Per the documentation, you could define the function for PlusMinus:

PlusMinus[a_] := {-a, a}
\[PlusMinus]2
(* {-2,2} *)
ListPlot[Table[\[PlusMinus]i, {i, 4}]]