Here is the graph of the function $f(x)$. As we discussed earlier, the function is continuous at $x = -2$ because the left-hand limit, right-hand limit, and the function's value at $x = -2$ all agree at $-4$, which can be seen on the graph (marked by the red dot at $(-2, -4)$).

Would you like further clarification on this, or do you have any other questions?

Here are 5 related questions for further exploration:

1. How do you determine if a piecewise function is differentiable at the boundary point?
2. What is the derivative of $f(x)$ for each piece of this piecewise function?
3. Can a function be continuous but not differentiable at a certain point? If so, provide examples.
4. How would you modify this function to make it discontinuous at $x = -2$?
5. How do limits play a role in determining continuity for more complex piecewise functions?

Tip: When analyzing continuity, always check the limits from both the left and right at any potential points of discontinuity.