Question

Whats the discontinuity of the function f(x) =x^2-3x-28 over x+4

Answer 1

Factor top
(x-7)(x+4)
we can factor out the (x+4) on top and bottom to get
f(x)=x-7
but wait, don't forget the x+4 (siince we factored it out, there is a hole there)
set that equal to 0
0=x+4
-4=x

evaluate f(-4) in new
f(-4)=-4-7
f(-4)=-11

so the hole is at (-4,-11)
the point of discontinuity is at (-4,-11)