For the domain is it x no equal to +/- 2 or all real numbers?

For the range is it (1, infinity)

I hope I'm understand this right

The domain consists of all the possible x values. At x=+/-2, y=0. Therefore, the function has output values when you put in 2 or -2. This means that -2 and 2 are in the domain.

x=0 is the only value that does not have an output (or corresponding y-value.) Because of this, x=0 is the only number that should not be included in the domain. Therefore, the domain is all real numbers not equal to x.

You're close on the range. The range should be $\displaystyle (-\infty,1)$

This is because the function has y-values all the way down at negative infinity, and moving up to 1 (but not including 1 because y=1 is a horizontal asymptote).

Does this help?