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Math Help - Essential & removable discontinuity

  1. #1
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    Essential & removable discontinuity

    where does the function f(x)=(2x^2-7x-15)/(x^2-x-20)
    have
    a) an essential discontinuity; and
    b) removable discontinuity?
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    where does the function f(x)=(2x^2-7x-15)/(x^2-x-20)
    have
    a) an essential discontinuity; and
    b) removable discontinuity?
    \frac{2x^2-7x-15}{x^2-x-20} = \frac{(2x+3)(x-5)}{(x+4)(x-5)}

    note that the factor (x-5) in the numerator and denominator will divide out ... f(x) has a removable discontinuity, also known as a "hole", at x = 5.

    f(x) has a vertical asymptote, a non-removable discontinuity, at x = -4.
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