Problem:
For the function

evaluate f(-2), f(2), and the limits at x = -2 and x = 2 including both left-hand and right-hand limits.

Visualization:
Using Maple:

First, we enter the function and then plot the graph:

> f:= x -> piecewise(x<=-2, -3-x, -2<x and x<=2, 2*x, x>2, x^2-4*x+3);

> plot(f(x),x=-4..4,discont=true);

We now let Maple do all of the calculations:

> f(-2);

- 1
> f(2);

4
> limit(f(x),x=0);

0
> limit(f(x),x=-2);

undefined
> limit(f(x),x=-2,left);

- 1
> limit(f(x),x=-2,right);

- 4
> limit(f(x),x=2);

undefined
> limit(f(x),x=2,left);

4
> limit(f(x),x=2,right);

-1