# 1.6 | Powers, Polynomials, and Rational Functions

If the graph of $$y = f(x)$$ approaches a horizontal line $$y = L$$ as $$x \rightarrow \infty$$ or $$x \rightarrow – \infty$$, then the line $$y = L$$ is called a horizontal asymptote. This occurs when
$$f(x) \rightarrow L \text{ as } x \rightarrow \infty$$
or
$$f(x) \rightarrow L \text{ as } x \rightarrow -\infty$$

If the graph of $$y = f(x)$$ approaches a vertical line $$x = K$$ as $$x \rightarrow K$$ from one side or the other, that is, if
$$y \rightarrow \infty \text{ or } y \rightarrow – \infty \text{ as } x \rightarrow K,$$
then the line $$x = K$$ is called a vertical asymptote.