Please help with this calculus problem!

Sketch the function f(x) = x / (x^2 - 9) without technology. Determine enough information to make an accurate graph. You should include intercepts details, asymptotes, extremas, points of inflection, and any other significant details, justifying your results with analytical methods.

Question

Please help with this calculus problem!

Sketch the function f(x) = x / (x^2 - 9) without technology. Determine enough information to make an accurate graph. You should include intercepts details, asymptotes, extremas, points of inflection, and any other significant details, justifying your results with analytical methods.

anonymous · Answer

I have to be able to do it without technology :/

anonymous · Answer

first do the non-calculus stuff...
x and y intercepts
horizontal vertical asymptotes
domain/range

then use calculus stuff like extremas, inflection to determine the shape of the graph in specific interval...

anonymous · Answer

you can notice that function gets +-infinity near 3 and -3 and is not defined at this points

anonymous · Answer

for the calculus part you'll need to take f' and f''

anonymous · Answer

Ok

anonymous · Answer

i think you could manage a general picture without that...

experimentx · Answer

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-10-curve-sketching/

anonymous · Answer

true...

anonymous · Answer

Ok guys, thanks for your help