Final answer:
The function f(x) = ((2x+1)(x-2))/(x(2x+1)) has two horizontal asymptotes: y = 2 as x approaches positive infinity and y = 2 as x approaches negative infinity.
Step-by-step explanation:
The function f(x) = ((2x+1)(x-2))/(x(2x+1)) has two horizontal asymptotes. To find them, we need to analyze the behavior of the function as x approaches positive and negative infinity.
As x approaches positive infinity, the terms (2x+1) and (x-2) become insignificant compared to the term x(2x+1). Therefore, the function approaches the horizontal asymptote y = 2.
As x approaches negative infinity, the terms (2x+1) and (x-2) become insignificant compared to the term x(2x+1). Therefore, the function approaches the horizontal asymptote y = 2.