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anonymous

  • one year ago

What is the vertical asymptote for the graph of y = x-2/(x-2)(x+3)?

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  1. anonymous
    • one year ago
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    i think that its x=-3 and x=2 ? right?

  2. mathmate
    • one year ago
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    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.

  3. mathmate
    • one year ago
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    Hint: simplify the rational function before attempting to locate asymptotes.

  4. anonymous
    • one year ago
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    It's the first equation

  5. mathmate
    • one year ago
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    Good, so follow the hints and see where they take you!

  6. anonymous
    • one year ago
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    I did simplify thats how I got x = -3

  7. mathmate
    • one year ago
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    What is the simplified version of the function, and what do you think the graph looks like?

  8. anonymous
    • one year ago
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    i think there is a hole so the answer might be (2, 1/5) ?

  9. mathmate
    • one year ago
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    Very good, the hole is at (2,1/5). Where do you think the asymptotes are?

  10. mathmate
    • one year ago
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    The function is now: f(x)=1/(x+3) where x\(\ne\)2 the hole (x=2) is not part of the domain.

  11. mathmate
    • one year ago
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    hint: Try to visualize where the asymptotes should be. If not ,use your graphs calculator

  12. mathmate
    • one year ago
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    Remember that an asymptote occurs when the denominator becomes zero.

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