Asymptote

A line that a curve approaches increasingly closely without reaching. For exponential growth and decay graphs, the $x$-axis, $y=0$, is a horizontal asymptote.

A straight line that a curve approaches increasingly closely without meeting.

A line that a curve approaches; the tangent graph has vertical asymptotes at angles where the function is undefined.

A line that a curve approaches without meeting; for $y=\frac{1}{x}$, both coordinate axes are asymptotes.

A line that a curve gets closer and closer to without meeting. For $y=k^x$ with $k>0$ and $k\ne1$, the $x$-axis is a horizontal asymptote.

A line that a curve gets closer to without reaching. A vertical asymptote marks an x-value where the curve is undefined.