As $\quad f(x) \rightarrow \pm \infty,\quad {1 \over f(x)} \rightarrow 0^\pm$ (vert asymptote at $f(x)=0$)
-As $\quad x \rightarrow \pm \infty,\quad {-1 \over x}$
+<!-- As $\quad x \rightarrow \pm \infty,\quad {-1 \over x}$ -->
- reciprocal functions are always on the same side of $x=0$
- if $y=f(x)$ has a local max|min at $x=1$, then $y={1 \over f(x)}$ has a local max|min at $x=a$
Cartesian equation for hyperbolas ($a$ and $b$ are dilation factors):
$${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
-Asymptotes at $y-k=\pm {b \over a}(x-h$)
+Asymptotes at $y=\pm {b \over a}(x-h)+k$
+To make hyperbola up/down rather than left/right, swap $x$ and $y$
## Parametric equations