The graph shows a discontinuity at $x = 0$. Let us determine the type of discontinuity by analyzing the graph:

1. At $x = 0$, the function has a jump discontinuity. This is because:
   • The left-hand limit ($\lim_{x \to 0^-} f(x)$) is 2.
   • The right-hand limit ($\lim_{x \to 0^+} f(x)$) is -3.
   • The limits do not match, so there is no continuity at $x = 0$.

Conclusion:

The discontinuity at $x = 0$ is a jump discontinuity.

Would you like a more detailed explanation or have further questions?

Here are 5 related questions to explore:

1. What are the other types of discontinuities, and how do they differ from a jump discontinuity?
2. How do you calculate the left-hand and right-hand limits of a piecewise function algebraically?
3. Can a function be integrable if it has jump discontinuities? Why or why not?
4. How do removable discontinuities appear on a graph?
5. What is the significance of discontinuities in real-world applications, such as signal processing?

Tip: Always check both the left-hand and right-hand limits to classify discontinuities properly!