# Asymptotes **Asymptotes:** Points of the function that are undefined and blow up to $\pm \infty$ before and after the asymptote's line. ![[Pasted image 20220521033847.png]] ### Vertical Asymptotes > [!summary]+ Formal Definition > Let $f(x)$ be a function. If any of the following conditions hold, then the line $x=a$ is a **vertical asymptote** of $f(x)$: > > $\lim_{x \to a^-}f(x)= \pm \infty$ > $\lim_{x \to a^+}f(x)= \pm \infty$ > $\text{or}$ > $\lim_{x \to a}f(x)= \pm \infty$ --- ### Horizontal Asymptotes > [!summary]+ Formal Definition > a > If x The horizontal asymptote can be found by comparing the degree of the numerator $M$ to the degree of the denominator $N$: - If $M < N$, then --- ### Oblique Asymptotes > [!summary]+ Formal Definition > 1 --- ## Finding Asymptotes Without Graphing