SOLUTION: find all numbers for which the rational expression is undefined q^3 - 5q/ q^2-9

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Question 208584: find all numbers for which the rational expression is undefined
q^3 - 5q/ q^2-9
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
equation is:
(q^3 - 5q) / (q^2-9)
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q^2 - 9 is the product of:
(q-3)
and
(q+3)
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since q^2 - 9 is in the denominator, this means that the denominator will be 0 when q = 3 and when q = -3
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when the denominator is 0, the equation is undefined, because the result of a division by 0 is undefined.
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a graph of your equation would look like this:
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graph%28600%2C600%2C-4%2C4%2C-30%2C30%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29
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a longer range view would be:
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graph%28600%2C600%2C-20%2C20%2C-40%2C40%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29
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the y values when x = -3 and when x = 3 are undefined because you can't divide a real number by 0 and get a real number as an answer.
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as x gets closer to 3 or -3, the value of y approaches infinity or minus infinity.
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the vertical lines you see are called asymptotes.
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the graph doesn't really show it all too well, but the y value goes way up or down as you approach x = 3 and x = -3. off the charts so to speak. if the resolution was a lot better, you would be able to see it a lot better.
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