College Algebra

study guides for every class

Asymptotes

Asymptotes are lines that a curve approaches but never touches or intersects. They provide insight into the behavior of the graph at extreme values.

congrats on reading the definition of asymptotes. now let's actually learn it.

Asymptotes can be vertical, horizontal, or oblique.
For hyperbolas, asymptotes intersect at the center and define the slope of the branches.
The equations of asymptotes for a hyperbola centered at $(h, k)$ with horizontal transverse axis are $y = k \pm \frac{b}{a}(x - h)$. For a vertical transverse axis, they are $y = k \pm \frac{a}{b}(x - h)$.
Asymptotes help to sketch hyperbolas accurately by providing guidelines for their branches.
Asymptotic behavior describes how functions behave as inputs approach infinity or specific values.