Diana R.

asked • 03/29/19

PreCalculus Questions... I need help now!

Which of the following statement are true for the graph of f(x)=(3x)/(x^3 -9x)

A) x=3 is the only vertical asymptote

B) The graph of function f has no horizontal asymptote.

C) x=3 and x=-3 are vertical asymptotes.

D) 1/3 is a horizontal asymptote.

E) x=0, x=3, and x=-3 are vertical asymptotes.


1 Expert Answer

By:

William W. answered • 03/29/19

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Diana R.

The actual equation is (3x)/(x^3 -9x). I accidentally forgot the other x, but thank you for answering. Would any of those statements be true with the real equation?
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03/29/19

William W.

Yes, Again the vertical asymptotes are when the denominator is zero. Setting x^3 - 9x = 0, you can factor out an x to get x(x^2 - 9) = 0 and then you can factor x^2 -9 into (x + 3)(x - 3) so it becomes (x)(x + 3)(x - 3) = 0. Set each piece equal to zero so you get vertical asymptotes at x = 0, x = -3, and x = 3 making E true
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03/29/19

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