Answer
No, $T$ is not a function, both because it does not map every value in the domain onto a value in the codomain, and because it maps some values in the domain onto multiple values in the codomain.
Work Step by Step
Note that this relation is the unit hyperbola. The values of $x$ on the interval $(-1,1)$ are not mapped into the codomain, and every value of $x$ less than -1 or greater than 1 is mapped onto two values in the codomain.
