This week I’m going to write about graphing a reciprocal function.

First of all, a reciprocal is an inverse of a fraction. Since every number is just the reciprocal would be  and a reciprocal function follows the same rule. For example would become 

To graph a function like this, whether it is quadratic or not, you’ll start by graphing the original function. Let’s just do a linear for this example. 

The original function is  So we graph that.

Then, once we have that we can begin to graph the reciprocal function. This is known as a hyperbola.

Firstly we’ll find the Invariant points. These points are at y=-1 and y=1. These points are important because the reciprocal is still equal to 1.

So we’ve got the invariants and now, we find the asymptotes. The asymptotes are borders, or lines, on the x-axis and y-axis of the graph that the hyperbola cannot pass.

This year in precalculus 11 the only x-axis intercept will be y=0, but the y-axis asymptote will pass through the x-intercept. In this case, it is at x=-3.

So, we have the asymptotes and we have the invariant points meaning we can graph the function. 

The Green and purple lines are the asymptotes. and as you can see the hyperbola will touch on each invariant points.