SOLUTION: Find the vertical asymptotes, if any, of the graph of the rational function. f(x) = x/x^2+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the vertical asymptotes, if any, of the graph of the rational function. f(x) = x/x^2+4      Log On


   

Question 818315: Find the vertical asymptotes, if any, of the graph of the rational function.
f(x) = x/x^2+4
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the function is
f(x) = x/x^2+4=x%2Fx%5E2%2B4=1%2Fx%2B4 graph%28300%2C300%2C-5%2C5%2C-5%2C15%2Cx%2Fx%5E2%2B4%29
there is a vertical asymptote, x=0.

If the function is
f(x) = x/(x^2+4)=x%2F%28x%5E2%2B4%29 graph%28300%2C300%2C-20%2C20%2C-0.5%2C0.5%2Cx%2F%28x%5E2%2B4%29%29
there is no vertical asymptote,
because the denominator, x%5E2%2B4 ,
is not zero for any real value of x .