Find the horizontal asymptote of 4x-8/(x-4)(x+1)
To find the horizontal asymptote of a function, we look at the limits as x approaches positive infinity and negative infinity.
As x approaches positive infinity, the term 4x becomes larger and larger compared to the terms (x-4)(x+1). Thus, we can ignore the terms (x-4)(x+1) because they become negligible compared to 4x. Therefore, the function approaches y = 4x as x approaches positive infinity.
As x approaches negative infinity, the term 4x becomes larger and larger in magnitude, but the terms (x-4)(x+1) also become larger and larger in magnitude. However, no matter how large the terms (x-4)(x+1) become, they will always remain small compared to the term 4x. Therefore, the function approaches y = 4x as x approaches negative infinity.
Thus, the horizontal asymptote of the function is y = 4x.