please help with this piecewise function problem

Question

(a) Sketch the graph of f on the interval [-2,2]

(b) Find all values of x in [-2,2] at which f is not continuous. Explain why

(c) Is f differentiable at x=0? Explain

Is f differentiable at x= -1? Explain

Answer 1

Each of the three pieces are continuous since they are all polynomials. Therefore, on those intervals, you won't ever have any holes or gaps. You might have holes or gaps between the functions though.

An example of this would be at x = 0.

Just to the left of x = 0, you have the function 3x+2. As x approaches zero on this function, y approaches 2.

To the right of the x = 0, you have the function -1. As x approaches zero on this function, y is -1

Therefore at x = 0, you'll have a gap, since y is dropping from 2 to -1.

You could probably see this from your sketch.

To check or differentiability, you have to do the same thing, but with f '(x)