Give an example of a function with both a removable and a non-removable discontinuity.

Question

Give an example of a function with both a removable and a non-removable discontinuity.

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Thu Giang 5 years 2021-07-25T10:52:18+00:00 1 Answers 97 views 0

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  1. Cherry
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    2021-07-25T10:53:48+00:00
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    Answer:

    (x+5)(x-3) / (x+5)(x+1)

    Step-by-step explanation:

    A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn’t exist at -5, but the x + 1 doesn’t have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )