Calculus (Discontinuities)
posted by Mishaka .
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?

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