Determine if the given function is continuous at x=a and if the function is differentiable at x=a

Question

Determine if the given function is continuous at x=a and if the function is differentiable at x=a

A.    Discontinuous and not differentiable at a

B.    Continuous and differentiable at a

C.    Discontinuous and differentiable at a

D.    Continuous and not differentiable at a

Answer 1

The piecewise function given has the graph above. In the given:

x=a=2.

In that case, y=2 and the point is along the straight line. Therefore it's both continuous and differentiable at x=a=2.