Question

Is there a hole in y=4x/x^3-4x

Answer 1

Hello Ramirez,

I assume that you meant to put parenthesis around the entire expression for the denominator: (x^3 - 4x). 

If so, then you would have a hole wherever the denominator is zero, because it would be undefined.

So let's factor: x^3 - 4x
First factor out an x to get x(x^2 - 4).
Then, we have the difference of squares, so we can factor it to: x(x+2)(x-2)

If we set that equal to zero, there are 3 possible solutions.

0, 2, and -2

These inputs would make the denominator zero and you would have a hole on your graph.

I hope this helps,
MrEQ