SOLUTION: Graph of the following rational functions,give any equations for vertical,horizontal,or oblique asymptotes. Label completely! 6+2x ------ -4+x

Question 77409: Graph of the following rational functions,give any equations for vertical,horizontal,or oblique asymptotes. Label completely!
6+2x
------
-4+x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If we have a 0 as our denominator, then we have a vertical asymptote, so...

So our vertical asymptote is

For our horizontal asymptote, we simply evaluate x for a very large values and see where it ends up. In other words:

Let x=1000

Let x=10,000

Let x=1,000,000
It looks like as we let x continue on forever, y will slowly approach the value of 2. So our horizontal asymptote is y=2. It turns out that we simply divide 2x by x to get 2
And since the degrees of the numerator and the denominator are the same, we will not have any oblique asymptotes.
So here's our graph:
graph of The vertical line is the vertical asymptote (it is not part of the graph) and the horizontal asymptote is the green line (it is not part of the graph also, it is used to show where the asymptote is).
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