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Math Help - continuity of a function at x=4

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    continuity of a function at x=4

    given:

    f(x)= ((x+2)/2), if x<4

    f(x)= ((13-x)/3) if x>4

    Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?
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    Quote Originally Posted by phalange View Post
    given:

    f(x)= ((x+2)/2), if x<4

    f(x)= ((13-x)/3) if x>4

    Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?
    Since the function is not defined for x = 4, how can it be continuous?
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    Quote Originally Posted by phalange View Post
    given:

    f(x)= ((x+2)/2), if x<4

    f(x)= ((13-x)/3) if x>4

    Is this function continuous at x=4? If not, is it removable discontinuity or non-removable discontinuity?
    These are 2 linear functions,
    one has a positive slope, the other negative.
    f(4) = 3 in both cases, if 4 was allowed in the domain.

    The "hole" at x=4 can be removed by filling it in,
    therefore it is a removeable discontinuity.

    The graph would then be continuous, albeit non-differentiable at x=4.
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