What does a horizontal asymptote describe?

What does a horizontal asymptote describe?

• A. It describes the end behavior of a function as x approaches infinity or negative infinity
• B. It describes the domain
• C. It is a vertical line
• D. It is only for polynomials

Answer: (A)

The key idea is end behavior: a horizontal asymptote is a horizontal line that the function’s values approach as x grows without bound in either direction. If the function has a horizontal asymptote y = L, then as x → ∞ or x → −∞, f(x) gets arbitrarily close to L. This describes how the graph behaves far out along the x-axis, not the domain or any vertical behavior. This is not about the domain, and a horizontal asymptote is not a vertical line (that would be a vertical asymptote). Also, horizontal asymptotes aren’t limited to polynomials—they can occur in many kinds of functions, depending on how their values stabilize at extreme x.

The key idea is end behavior: a horizontal asymptote is a horizontal line that the function’s values approach as x grows without bound in either direction. If the function has a horizontal asymptote y = L, then as x → ∞ or x → −∞, f(x) gets arbitrarily close to L. This describes how the graph behaves far out along the x-axis, not the domain or any vertical behavior.

This is not about the domain, and a horizontal asymptote is not a vertical line (that would be a vertical asymptote). Also, horizontal asymptotes aren’t limited to polynomials—they can occur in many kinds of functions, depending on how their values stabilize at extreme x.