This week we learned about graphing reciprocal functions.

A reciprocal is when you divide one by whatever you are given. For example:

Regular:

y = x + 4

Reciprocal:

y = \frac {1}{x+4}

When you graph one of these reciprocal functions you end up with a hyperbola.

Here is an example of the linear reciprocal function y = \frac {1}{x-5}

The two red curves you see are all of the solutions and are called the hyperbola.

The two locations where the original line crosses 1 and -1 are the invariant points, and they are the two spots that don’t change when reciprocated.

The two dotted black lines that determine the non-solutions are called asymptotes. The vertical one goes directly through the middle of the two invariant points, and the horizontal one is the x-axis.

Another thing to note is the vertical asymptote will always go through the x-intercept, and it is important to remember the asymptotes are completely separate from the x-y axis.

The hyperbolas converge on the asymptotes but will never actually reach them.