# How do you graph #f(x)=(x^2-2x)/(x^2-4)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

Jun 18, 2017

We can factor

#f(x) = (x(x - 2))/((x + 2)(x - 2))#

#f(x) = x/(x+ 2)#

This means that there will be a hole at

The horizontal asymptote will occur at the ratio between the highest power in the numerator and in the denominator (only if the powers are equal).

Hence, there will be a horizontal asymptote at

As for intercepts, the graph will pass through the origin, and the origin will serve as the x and y intercept.

Here is the graph:

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

Hopefully this helps!