Final answer:
A function can cross a horizontal asymptote when it intersects or passes through the asymptote line. For example, the function f(x) = 1/x crosses the horizontal asymptote y=0 at x=0.
Step-by-step explanation:
A function can cross a horizontal asymptote when the graph of the function intersects or passes through the line representing the asymptote. This can occur when the function approaches the asymptote from below and then crosses over to above it, or when the function approaches the asymptote from above and then crosses over to below it.
For example, consider the function f(x) = 1/x. As x approaches positive infinity, f(x) approaches zero from above. However, as x approaches negative infinity, f(x) approaches zero from below. Therefore, the graph of f(x) crosses the horizontal asymptote y = 0 at x = 0.