SOLUTION: Graph: {{{ y=(x^2-4)/(x^2+8x+15) }}} I'm a little confused as to how I go about doing this. What are the asymptotes? What points should I plot? How should this graph look? I have

Question 834884: Graph:
I'm a little confused as to how I go about doing this. What are the asymptotes? What points should I plot? How should this graph look? I have tons of problems like this one to do, so seeing how this one is done will help me out with the others. Thank you!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Look for vertical and horizontal asymptotes first.
Since

, the horizontal asymptote (as x approaches infinity) will be at x = 1. Same thing happens when x goes to negative infinity.
Set the denominator equal to zero to find possible vertical asymptotes. The equation

gives x = -3, -5 as roots. The numerator is nonzero in both cases, so those are your vertical asymptotes.
To graph, just note the asymptotes and whether the function approaches +/- infinity as x goes to -3 or -5 in either direction. Note that x = 1 is the horizontal asymptote.
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