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) = 5,  x does not equal 0

          3,  x=0                        a = 0

Answer 1

Near zero, f(x) is always five, but at zero, f(0) is three.  So this is a REMOVABLE discontinuity (the point (0,3) is not continuous with the rest of the graph, where y is always 5.  (The left & right limits are 5, as x approaches 0.)