How Do I Find the Asymptotes of a Function?

[donjt81]

ok so i have this problem where i am asked to find the asymptotes. It is kinda throwing me off because it is in the middle of the differentiation section. so here is the problem

problem: use the graphing strategy to sketch the graph of y=(4x)/(x^2+1). check for domain values, intercepts, asymptotes, critical values, interval where the function is increasing and where it is decreasing, intervals where it is concave up and where it is concave down. Then graph it. please use sign charts.

I have done all the other stuff but I don't know how to find the asymptotes. Can someone help please.

 

[Max Eilerson]

To find the horizonal asmptotes, you need to first factor the f(x) or y function (already done in your case), and then look at the co-efficients of the largest power of x in the numberator and denominator. $$f(x) = ax^m / bx^k$$. Then if
1.m < k, the asymptote is at y= 0.
2. m = k, the asymptote is at a/b
3. m > k, there is no asymptote

For vertical asymptotes, you need to find where the function goes to infinity (i.e. the value of x for which the denominator equals zero). I'm not sure what a complex asymptotes means.

 

[donjt81]

what is k?

 

[Max Eilerson]

Just edited it, n = k.