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

Algebra ->  Rational-functions -> 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       Log On


   

Question 834884: Graph: +y=%28x%5E2-4%29%2F%28x%5E2%2B8x%2B15%29+
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) About Me  (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.