document.write( "Question 57096: How do I graph the following rational function:
\n" ); document.write( "f(x)= 1/x^2+4\r
\n" ); document.write( "\n" ); document.write( "Thank you for your help. \n" ); document.write( "
Algebra.Com's Answer #38826 by funmath(2933)\"\" \"About 
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How do I graph the following rational function:
\n" ); document.write( "\"f%28x%29=1%2F%28x%5E2%2B4%29\"\r
\n" ); document.write( "\n" ); document.write( "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.
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\n" ); document.write( "Notice that this function can never=0 because the numerator cannot=0, there is a horizontal asymptote at y=0.
\n" ); document.write( "There is nothing that can make the denominator (x^2+4) =0, so there are no vertical asymptotes.
\n" ); document.write( "If x=0, f(0)=1/4, that's the tallest the graph will get.
\n" ); document.write( "F(-x)=f(x), so the graph is symmetric to the y axis.
\n" ); document.write( "The bigger x get's the smaller the function gets. It approaches 0 as x aproaches - infinity and + infinity.
\n" ); document.write( "The graph looks like:
\n" ); document.write( "\"graph%28300%2C200%2C-3%2C3%2C-2%2C2%2C1%2F%28x%5E2%2B4%29%29\"
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "
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