Hyperbolic Function

This is a regular hyperbola ( $y = \frac{a}{x}$ ), where $a = 1$ on the image above.

$a$ is the scale factor, and if it goes up, the distance between the hyperbola and the origin $(0, 0)$ increases.

Here is the generic hyperbola equation that is translatable:

$y = \frac{a}{x - p} + q$

where $(p, q)$ is the vertex coordinate of the parabola.

However, when translating, you must invert the signs for $p$ (try it yourself online!)

If there are no domain(s)/range(s):

$x\in real,\space x \neq p$$$$y\in real,\space y \neq q$

$y = \frac{1}{x - 3} + 2$

Translated graph with asymptote (blue).

Asymptote = $x = 3$ , and $y = 2$ .

ℕBTS