best description on figuring out if this is jump, infinite, continous, or removable

Question

g(x)= {1/(x-2) if x<1

{2x-4 if x> or equal to 1

Answer 1

Graph it. You get a cusp at x = 1.293 (estimated). This is continuous but not differentiable at that point. Otherwise, there is no discontinuity in this piecewise function.

Answer 2

It is a jump discontinuity.

 

As x approaches 1 from the left  (x<1)

g(x) approaches -1

 

As x approaches 1 from the right (x>1)

 g(x) approaches -2.

 

Since the left and right side limits do not agree,

  the g(x) has a jump discontinuity