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Math Help - Calc 1

  1. #1
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    Exclamation Calc 1

    Hi, so I'm new to this site but I am having a lot of confusion with the following question,

    Find all values of x, if any, for which the following function is not continuous


    f(x) =
    (1/2)x - 1, when x <= 2
    3 - x, when 2 < x <= 5
    x^2 - 27, when x > 5
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  2. #2
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    Re: Calc 1

    All three parts of this hybrid function are polynomials, and polynomials are known to be continuous everywhere.

    So the only places where this hybrid function might not be continuous are the points where it goes from one part to the next.

    So test what value the function approaches from the left and from the right of each of these points. See if they match...
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  3. #3
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    Re: Calc 1

    What do you mean when you say test what value the function approaches from the left and from the right of each of these points?
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  4. #4
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    Re: Calc 1

    For example, at x=2, you need to evaluate \lim_{x\to 2-} \frac{1}{2}x-1 = \frac{1}{2}(2)-1 = 0 and \lim_{x\to 2+} 3-x = 3-2 = 1. Since they don't match, the combined function is not continuous at x=2. If you graph the function, it will jump from 0 to 1 as you move to the right across x=2.

    - Hollywood
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