## Discrete Mathematics with Applications 4th Edition

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.
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.