# How do you graph #f(x)=x^2/(x-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

See explanation...

#### Explanation:

Alright, So for this question we are looking for six items - holes, vertical asymptotes, horizontal asymptotes,

graph{x^2/(x-1 [-10, 10, -5, 5]}

Right off the bat you can see some strange things happening to this graph. Lets really break it down.

To begin, lets find the

For the

Therefore,

Next, lets work on the asymptotes. To find the vertical asymptotes, set the denominator equal to

So we just found that there is a vertical asymptote at

There are three general rules when talking about a horizontal asymptote.

1) If both polynomials are the same degree,divide the coefficients of the highest degree term.

2) If the polynomial in the numerator is a lower degree than the denominator, then

3) If the polynomial in the numerator is a higher degree than the denominator, then there is no horizontal asymptote. It is a slant asymptote.

Knowing these three rules, we can determine that there is no horizontal asymptote, since the denominator is a lower degree than the numerator.

Finally, lets find any holes that might be in this graph. Now, just from past knowledge, we should know that no holes will appear in a graph with a slant asymptote. Because of this, lets go ahead and find the slant.

We need to do long division here using both polynomials:

I'm sorry that there isn't a great way to show you the long divition there, but if you have anymore questions about that, click here.

So there you go, I really hope this helped, and I apologize for the length!

~Chandler Dowd