Honors Mathematics 3 Practice Exam

What does a horizontal asymptote describe?

It describes the end behavior of a function as x approaches infinity or negative infinity It describes the domain It is a vertical line It is only for polynomials

Correct Answer:

It describes the end behavior of a function as x approaches infinity or negative infinity

Explanation:

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.

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