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9 October, 00:54

Find the key number to the equation, the intervals into which the key numbers divide the number line, and the sign of y over each of these intervals. y=x+1 / (x-1) ^2

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  1. 9 October, 02:55
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    The function seems to be y = (x+1) / (x - 1) ^2

    1) key number

    The key number (also called critical values) is where the denominator equals zero.

    (x - 1) ^2 = 0 = > x = 1

    2) intervals: (-∞,1), (1,∞)

    3) Sign of the function

    The sign of the denominator is always positive, then the sign of the function is the same sign of the numerator

    x + 1 > 0 = > x > - 1

    x + 1 x < - 1

    Then in the interval (-∞,1) the function is negative for (-∞,-1) and positive for (-1,1).

    The function is positive for all the values in the interval (1,∞)

    Briefle, the functionis negative in (-∞,-1) and positive in (-1,∞).
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