The horizontal asymptotes are the values to which the function approaches as x becomes larger and larger (+/- infinity).
Then you have to find the limits of the function for x -> + and – infinity.
If the limit does not exist then there is not horizontal asypmtotes.
Indeed the limit of that function when x goes to +/- infinity does not exist, because the denominator will continue fluctating between 1 and 2, and the numerator will be fluctuating between -1 and 1.
This function fluctuates periodically from negative infinity to positive infinity, it does not have a limit when x grows so it does not have horizontal asymptotes.