Sketch a possible accurate graph of the function described:
"f(x) is continuous for all x except x=1, where f has a nonremovable

To sketch a graph for the function described by the following key points:
- \( f(x) \) is continuous for all \( x \) except at \( x = 1 \).
- At \( x = 1 \), the function has a **nonremovable discontinuity**.

### Steps to Sketch the Graph:

1. **Continuity Everywhere Except \( x = 1 \):**
   - The graph should be smooth and connected at all points except at \( x = 1 \). A continuous curve should be drawn for the rest of the domain.

2. **Nonremovable Discontinuity at \( x = 1 \):**
   - A **nonremovable discontinuity** suggests that the graph has a break at \( x = 1 \) that cannot be fixed by filling a hole or redefining the function at \( x = 1 \). This could be either:
     - **Jump Discontinuity**: Where the function approaches two different values from the left and right sides of \( x = 1 \).
     - **Infinite Discontinuity**: Where the function approaches infinity or negative infinity at \( x = 1 \).

### Possible Graph Description:
- Draw a smooth curve on either side of \( x = 1 \).
- At \( x = 1 \), show a break in the graph, which could manifest as:
  - A **jump discontinuity**, where there is a clear shift in the function's value as \( x \) approaches 1 from the left and right.
  - Or an **infinite discontinuity**, where the graph approaches vertical asymptotes from one or both sides.

Would you like me to create a visual sketch of the graph based on these descriptions?

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**Relative Questions:**
1. What is the formal definition of a nonremovable discontinuity?
2. How do jump discontinuities differ from removable discontinuities?
3. Can a function have more than one type of discontinuity at the same point?
4. How can limits be used to classify discontinuities in functions?
5. How do nonremovable discontinuities affect the integrability of a function?

**Tip:** Nonremovable discontinuities often indicate that a function can't be made continuous at a point, no matter how it's redefined at that point.

Sketch a possible accurate graph of the function described: 'f(x) is continuous for all x except x=1, where f has a nonremovable discontinuity.'

Learn how to sketch a graph of a function that is continuous everywhere except at x=1, where it has a nonremovable discontinuity. This tutorial covers key concepts in continuity and discontinuity, providing a step-by-step approach to understanding different types of discontinuities, including jump and infinite discontinuities.

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