# How do you graph #f(x)=(2x-1)/(x^3-9x)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

x intercept:

y intercept:

vertical asymptotes:

horizontal asymptotes:

#### Explanation:

FIRST thing we ALWAYS do is making the function easier:

Now we can "easily" see that

We can also see that

vertical asymptotes:

Therefore we now know that the function has 3 vertical asymptotes (we get them when

horizontal asymptotes:

(I don't know if you know how to use

horizontal asymptotes is a question of a kind of "What does the function "act" when

To solve it easily, lets check with a calculator what happens when x comes is really big, for example I will check the positives:

So, the function goes to

On the same way, we can chek the very negative x-es:

So, in that case, the function goes to

therefore, the horizontal asymptote is:

x and y intercepts:

Now that we have an "easier" function:

We check both "x=0" and y=0":

But we already knew it because

Now lets check what if

So we have only one point