One of the things we learned this week in Precalc 11 is how to graph reciprocal of functions.

Hyperbola

Whenever we solve for a reciprocal of a function we will always get a hyperbola of some sort.

Linear

Quadratic

Graphing Reciprocal of Functions

Linear

The first step of graphing a reciprocal of linear function is to graph the original function first.

Next, we determine the invariant points (y=1 and y=-1)

Then we can determine the horizontal asymptote (y=0) and vertical asymptote (x-intercept).

The last thing to do is to draw the hyperbola, which is difficult to draw.

Quadratic

First step of graphing the reciprocal of a quadratic function is to graph the original function.

Next, determine the invariant points (y=1, y=-1)

Then we draw the horizontal asymptote (y=0) and the vertical asymptotes (x-intercepts).

The last thing would be to draw the hyperbola which could be tricky since there are many types of hyperbola for reciprocal of quadratic functions.