Which statement describes a horizontal asymptote?

• A. Side to side lines that are invisible that the graph will never touch
• B. Vertical lines that the graph will never touch
• C. The vertex of the parabola
• D. The x-intercept

Answer: (A)

Horizontal asymptotes describe how a function behaves far out toward positive or negative infinity. The idea is that the graph gets arbitrarily close to a horizontal line y = c as x grows without bound in either direction. That left-right line represents a constant y-value that the graph approaches in the tails. The other ideas point to different features: vertical lines where the graph shoots off to infinity, the x-intercept where the graph crosses the x-axis, or the vertex of a parabola. So the description of horizontal, side-to-side lines that the graph approaches as x goes to ±∞ captures the concept.