# How do you graph and find the discontinuities of #F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)#?

##### 1 Answer

Solve for the asymptotic discontinuities

#### Explanation:

To make it easier to look for the discontinuities, it helps to completely factor all the expressions first.

The discontinuities of a rational function are asymptotic discontinuities. These are the values of of

We can separate this into two equations:

Equation 1:

Equation 2:

The asymptotes are

As for graphing, you can do that by creating a table of values.

It should end up like this:

graph{(-2x^2+1)/(2x^3+4x^2) [-10, 10, -5, 5]}

You will notice that the graph looks like it's approaching x=0 and x=-2, but it will never actually touch it.