# Calculus (Discontinuities)

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Suppose,
f(x) = { (x - 1)^2 / x + 1 if x < 2
(x^2 - 2x - 8)/(x - 4) if
2 </= x < 4
(1 / (x - 3)) + 5) if 4 </=
x
Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump discontinuities.
When I graphed this function on my calculator, I found that there was definitely a jump discontinuity at x=4. There is, as far as I can see, one more discontinuity at -1, it looks as though it might be an infinite discontinuity since it is a vertical asymptote. Is this correct?

• Calculus (Discontinuities) -

That is correct. f(-1) = 4/0 which is infinite.

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