https://file.aiquickdraw.com/mathbot/file/1726447525018dwjb3ptm.jpg

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



 

The field below accepts a list of numbers or formulas separated by semicolons (e.g.  2;4;6
  or  x+1;x−1
 ). The order of the list does not matter.

The graph represents a function, and we are asked to determine the values of \( x \) at which the function is not continuous.

Based on the visual inspection of the graph, here are the key observations:

1. There is a **vertical asymptote** near \( x = -5 \), which suggests that the function is not continuous at \( x = -5 \).
2. There is an **open circle** on the graph near \( x = 4 \), indicating a discontinuity at \( x = 4 \), as the function is not defined at this point.

### Conclusion:
The function is not continuous at:
\[
x = -5 \quad \text{and} \quad x = 4
\]

Would you like any further details or have any questions?

### Related questions:
1. What are the types of discontinuities (e.g., jump, removable, infinite) at \( x = -5 \) and \( x = 4 \)?
2. How can the concept of limits explain the discontinuity at \( x = -5 \)?
3. Can you describe the difference between a removable discontinuity and an essential discontinuity?
4. How can you determine if a function is continuous using its derivative?
5. What does it mean for a function to be continuous on a closed interval?

### Tip:
Discontinuities in a function can often be identified through vertical asymptotes or gaps in the graph, so it's important to check for these when analyzing continuity.

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

Analyze the graph to determine where the function is not continuous. The function has a vertical asymptote at x = -5 and an open circle indicating a removable discontinuity at x = 4. This is a common problem in high school calculus or pre-calculus courses.

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