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Question 191629: graph 
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! In order to graph , we need to determine the horizontal and vertical asymptotes (think of these as the boundaries that will contain the graph)
Horizontal Asymptote:
Take note that the degree of the numerator is 0 and the degree of the denominator is 1. Since the degree of the numerator is smaller than the degree of the denominator, this tells us that the horizontal asymptote is 
Note: whenever the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is ALWAYS
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Vertical Asymptote:
Start with the given equation.
 Set the denominator equal to zero (remember, division by zero is NOT defined, which is why a vertical asymptote arises)
 Add 2 to both sides.
So the vertical asymptote is
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So we now know that the horizontal and vertical asymptotes are and , we can plot the asymptotes:
Graph of the asymptotes (blue) and (red)
Now all we need to do is determine where the graph lies. So let's see where the graph lies when  (ie to the left of the vertical asymptote)
So plug in  :
Start with the given equation.
 Plug in
 Combine like terms.
 Reduce
Since this value is less than the horizontal asymptote, this tells us that the potion of the graph to the left of the vertical asymptote is BELOW the horizontal asymptote.
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Now plug in a value that is to the right of . Let's plug in 
Start with the given equation.
 Plug in
 Combine like terms.
 Reduce
Since this y value is greater than the horizontal asymptote, this means that EVERY point to the right of the vertical asymptote is ABOVE the horizontal asymptote.
So what we've determined is the graph goes through the points (0,-2) and (3,4). Let's plot them:
Now draw a hyperbola (it doesn't need to be perfect) through these points like so:
Graph of
Answer by stanbon(75887) (Show Source):
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