For the given function, ƒ, determine if the function is discontinuous at a given point. State which condition of continuity fails or state the function is conti

Question

For the given function, ƒ, determine if the function is discontinuous at a given point. State which condition of continuity fails or state the function is continuous at x = a.

f(x) = x/lxl, a = 0

Answer 1

f(x) = x/lxl is CONTINUOUS EVERYWHERE except at x = 0 because division by zero is prohibited.  Zero is not in its domain; the function is continuous on its domain.  At 0, there's a JUMP discontinuity because for negative x values, f(x) = -1 but for positive x values, f(x) = 1.