Piecewise function graph showing two parabolic sections with discontinuities at specific points.

Final Answer:
The function is discontinuous at $ x = -4 $, $ x = 2 $, and $ x = 4 $.

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Explanation:
We look for points where the graph “breaks” — meaning the function isn’t smooth or connected there.

1. At $ x = -4 $:
There’s a solid dot (meaning the function *has* a value there), but the curve approaches from the left and doesn’t connect to that dot — it jumps. So it’s a jump discontinuity.

2. At $ x = 2 $:
There’s a solid dot at $ (2, -1) $, but the curve comes down from above and stops just before $ x = 2 $, then jumps to the dot. Again, not connected → discontinuity.

3. At $ x = 4 $:
There’s an open circle (meaning the function is *not defined* there), and the curve approaches from both sides but doesn’t include that point. That’s a removable discontinuity (a hole), still a discontinuity.

Other points (like $ x = -1 $, $ x = 0 $, etc.) have no breaks — the curve passes smoothly through them, even if it changes direction.

So the function is discontinuous exactly at $ x = -4 $, $ x = 2 $, and $ x = 4 $.