Question

Determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = 3 / x2 + 4
jump discontinuitiesx=
removable discontinuitiesx=
infinite discontinuitiesx=
other discontinuitiesx=

Answer 1

jump discontinuities x= DNE

removable discontinuities x= DNE

infinite discontinuities x= -2, 2

other discontinuities x= DNE

The function has an infinite discontinuity at x=-2 and x=2 because the denominator of the fraction, x^2 + 4, approaches 0 as x approaches -2 or 2.