find the values of a such that lim f(x) does not exist and where f(x) is discontinuous at x=a

Question

Consider the function f, defined by:

f(x)={

-x if x<-1

sin((pi/2)x) if -1≤x<1

2 if x=1

2-x if x>1

1. Find the values a such that lim (as x approaches a) f(x) does not exist
2. Find the values of a such that f(x) is discontinuous at x=a

Answer 1

Here is the graph:

The limit does not exist at x = -1

The function is not continuous at a = -1 and at x = 1

Answer 2

This function has four pieces to it. Can you graph each of the pieces individually and then restrict them to build the complete function?

For the questions, we really just need to investigate what happens around -1 and 1.