# How do you graph #(6x)/(x^2-36)# using asymptotes, intercepts, end behavior?

##### 1 Answer

Vertical asymptotes at

As

As

#### Explanation:

Let a minute amount of

I have deliberately used this symbol as in introduction to calculus without actually using calculus

Set to

Notice that the denominator is the difference of two squares. So we have:

Note that the use of

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This becomes 'undefined if the denominator is zero thus we have vertical asymptotes at those points.

Vertical asymptotes at

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Let

Set

Now

...................................................................................................

Let

Following the same methodology of thinking we find that in this case the denominator is only just smaller than 0 so when divide into the numerator the whole is tending to

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As in the processes above:

When

When

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As

The net consequence is that

For

For