From the graph you have provided, the function appears to have discontinuities at specific points where the graph is either interrupted, jumps, or contains holes.

Discontinuities:

1. At $x = -5$: There is a vertical asymptote, indicating a discontinuity where the function approaches infinity or negative infinity. The graph sharply dips downwards toward $-\infty$ from the left of $x = -5$ and continues from above after $x = -5$, which suggests the function is not defined at $x = -5$.

2. At $x = 7$: There is a small circle or "hole" in the graph, meaning the function is not defined at this exact point, despite the function continuing smoothly elsewhere.

Conclusion:

The function is not continuous at $x = -5$ and $x = 7$. These are the points where the function either has an asymptote or a hole.

Would you like further details or explanations about these discontinuities? Here are five related questions to deepen your understanding:

1. What is the definition of a discontinuous function?
2. How do asymptotes relate to discontinuities in a function?
3. What types of discontinuities exist (e.g., removable, jump, and infinite discontinuities)?
4. How can you determine if a function has a removable discontinuity?
5. What role do limits play in identifying discontinuities in functions?

Tip: In cases where a function appears to have a hole, the discontinuity may be removable if the function can be redefined to fill that hole!