we are given the following function:

In order to find the horizontal asymptote we need to solve for "y". To do that we will give values of "x" that are negative:
For x = -1 we have:

For x = -5

For x = -8

For x = -10

If we continue giving values of "x" that are smaller and smaller we see that the value of the function tends to be 0, therefore, the horizontal asymtote for this function is y = 0.