Asymptotes

### 1.2 Asymptotes

We say a line is an asymptote of a curve if the distance between the line and the curve approaches zero as the curve (specifically the $$x$$ or $$y$$ coordinates of the points on the curve) goes to $$+\infty$$ or $$-\infty$$.

We study three types of asymptotes: (1) vertical, (2) horizontal, and (3) oblique (or inclined or slant).

#### Vertical Asymptotes

The line $$x=a$$ is a vertical asymptote of the graph of $$f$$ if $$f(x)\to +\infty$$ or $$f(x)\to -\infty$$ as $$x$$ approaches $$a$$ from the left or right.

See Figure 1.2.1.