# Functions, Graphs, and Limits

# Slant Asymptotes

A **slant asymptote**, also known as an **oblique asymptote**, is an asymptote that's a straight (but not horizontal or vertical) line of the usual form *y* = m*x* + b (in other words, a degree-1 polynomial). A function with a slant asymptote might look something like these:

If a function *f*(*x*) has a slant asymptote as *x* approaches ∞, then the limit does not exist, because the function must grow without bound to stay close to the slant asymptote.