anonymous
  • anonymous
What is the vertical asymptote for the graph of y = x-2/(x-2)(x+3)?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
i think that its x=-3 and x=2 ? right?
mathmate
  • mathmate
There is an ambiguity with the rational function, not sure if it is \(\large y = \frac{x-2}{(x-2)(x+3)}\) or \(\large y = \frac{(x-2)}{(x-2)}(x+3)\) According to the rule PEMDAS, it's the second, but I think you meant the first.
mathmate
  • mathmate
Hint: simplify the rational function before attempting to locate asymptotes.

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anonymous
  • anonymous
It's the first equation
mathmate
  • mathmate
Good, so follow the hints and see where they take you!
anonymous
  • anonymous
I did simplify thats how I got x = -3
mathmate
  • mathmate
What is the simplified version of the function, and what do you think the graph looks like?
anonymous
  • anonymous
i think there is a hole so the answer might be (2, 1/5) ?
mathmate
  • mathmate
Very good, the hole is at (2,1/5). Where do you think the asymptotes are?
mathmate
  • mathmate
The function is now: f(x)=1/(x+3) where x\(\ne\)2 the hole (x=2) is not part of the domain.
mathmate
  • mathmate
hint: Try to visualize where the asymptotes should be. If not ,use your graphs calculator
mathmate
  • mathmate
Remember that an asymptote occurs when the denominator becomes zero.

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