f(x)=(2x^2+5x-12)/(x^2-3x-28)
Is this function continuous at x=7? If not which condition does it fail?
Note that
f(x) = (2x-3)(x+4) / (x-7)(x+4)
So f(x) is not continuous at x=7, since division by zero is undefined.
f(x) is also not defined at x = -4, but that discontinuity can be removed by defining f(-4) = 1, since f(x) = (2x-3)/(x+4) everywhere except at x = -4 or 7.