https://file.aiquickdraw.com/mathbot/file/1726102410229a87ntzec.jpg

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!

Use the graph to determine the values of x at which the function is not continuous.

Learn how to identify discontinuities in a graph. This example shows discontinuities at x = -5 (vertical asymptote) and x = 7 (removable discontinuity), making it ideal for students in Grades 10-12.

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