SOLUTION: How do I graph the following rational function: f(x)= 1/x^2+4 Thank you for your help.

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Question 57096: How do I graph the following rational function:
f(x)= 1/x^2+4
Thank you for your help.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
How do I graph the following rational function:
f%28x%29=1%2F%28x%5E2%2B4%29
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%28300%2C200%2C-3%2C3%2C-2%2C2%2C1%2F%28x%5E2%2B4%29%29
Happy Calculating!!!