4.19 Asymptotes

An asymptote to a curve is a straight line that becomes close to the curve as $x$ or $y$ tends to $\pm\infty$. Some authors write $f(x)\asymp ax+b$ as $x\rightarrow\infty$ to mean that the line $y=ax+b$ is an asymptote to the graph of $f$ as $x\rightarrow\infty$.

When sketching a graph, draw the asymptotes first, since straight lines are easy to draw, then draw the graph approaching the asymptote.