The discontinuities in graphs (a) and (b) are removable discontinuities because they disappear if we define or redefine f at a so that The function in graph (c) has a jump discontinuity because left and right limits exist at a but are unequal. The discontinuity in graph (d) is an infinite discontinuity because the function has a vertical asymptote at a.

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f(a) = lim f(x). х- УА y = f(x) y = f(x) Removable Removable discontinuity discontinuity a х х (a) (b) УА УА Jump discontinuity y = f(x) y = f(x) Infinite discontinuity + х х (c) (d)