Question 57096
How do I graph the following rational function:
{{{f(x)=1/(x^2+4)}}}

If you are taking Calculus, you have to use derivatives rather than reasoning.  Let me know if that's what you're taking.  I added parenthesis where I thought they would be, let me know if you didn't intend them.
:
Notice that this function can never=0 because the numerator cannot=0, there is a horizontal asymptote at y=0.
There is nothing that can make the denominator (x^2+4) =0, so there are no vertical asymptotes.
If x=0, f(0)=1/4, that's the tallest the graph will get.
F(-x)=f(x), so the graph is symmetric to the y axis.
The bigger x get's the smaller the function gets.  It approaches 0 as x aproaches - infinity and + infinity.
The graph looks like:
{{{graph(300,200,-3,3,-2,2,1/(x^2+4))}}}
Happy Calculating!!!