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.

E 1.6 Exercises