Final answer:
The horizontal asymptote for the function f(x) = -2/(x-5) - 2 is the constant term -2, so the equation of the asymptote is y = -2.
Step-by-step explanation:
The horizontal asymptotes of a function are the values that the function approaches as x goes to +/- infinity. For the function f(x) = -2/(x-5) - 2, we can determine its horizontal asymptotes by examining the behavior of x as it goes to infinity. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the constant term of the function's simplified form when x approaches infinity.
In this case, as x becomes very large or very negative, the -2/(x-5) part approaches 0, and the horizontal asymptote is simply the constant term, -2. Therefore, the equation of the horizontal asymptote is y = -2.