In order to prove that a function is bijective, we must show that it is both injective (one-to-one) and subjective (onto). Let's see if this function is.
In order to be injective, two values in the domain cannot map to the same value in the co-domain. More formally, for all x,y in the domain, f(x) = f(y) implies that x = y. We can see that this function is not injective by a simple counter-example. We can see that f(2) = f(-2) = 0 but clearly 2 doesn't equal -2. Since two values in the domain both map to 0, it's not an injection.
In order to be surjective, it must be true that the function maps to every value in the co-domain. More formally, for all y in the co-domain, there must be an x in the domain such that f(x) = y. The maximum value in the co-domain obtained by this function is 8 so there are many counter-examples. For example, 10 is in the co-domain but there are no values x in the domain such that f(x) = 10, so it's not a surjection.
This function fails both of the requirements to be bijective so it is not.