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

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

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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(21667) About Me  (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...

-4%2Bx=0
x=4
So our vertical asymptote is x=4

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

%286%2B2%281000%29%29%2F%28-4%2B1000%29=2.0140562248996 Let x=1000

%286%2B2%2810000%29%29%2F%28-4%2B10000%29=2.00140056022409 Let x=10,000

%286%2B2%281000000%29%29%2F%28-4%2B1000000%29=2.000014000056 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%28+300%2C+200%2C+-6%2C+15%2C+-10%2C+10%2C+%286%2B2x%29%2F%28-4%2Bx%29%2C+2%29+ graph of y=%286%2B2x%29%2F%28-4%2Bx%29 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).