https://file.aiquickdraw.com/mathbot/file/1726892777932wc7b1d94.jpg

https://file.aiquickdraw.com/mathbot/file/1726892777932ezypq9s7.jpg

Let's analyze the graph and the multiple-choice answers one by one:

1. **Option A: \( f(0) = 1 \)**  
   Looking at the graph at \( x = 0 \), the value of \( f(0) \) is approximately 1, as there is no hole or discontinuity. So, **Option A is true**.

2. **Option B: \( f(1.5) \) is undefined**  
   At \( x = 1.5 \), the graph shows an open circle, indicating that the function is undefined at this point. So, **Option B is true**.

3. **Option C: \( f(-1) \) is undefined**  
   At \( x = -1 \), the graph is continuous with no open circles or discontinuities. There is a defined value at \( x = -1 \), which is around 2. Hence, **Option C is false**.

4. **Option D: \( \lim_{x \to 1} f(x) = 2 \)**  
   As \( x \) approaches 1 from both sides, the graph tends to the value 2. Therefore, the limit exists and is equal to 2. So, **Option D is true**.

5. **Option E: \( \lim_{x \to 0^+} f(x) = 1 \)**  
   The right-hand limit as \( x \) approaches 0 from the positive side gives a value of 1. So, **Option E is true**.

### Conclusion:
The false statement is **Option C**: \( f(-1) \) is **not** undefined.

Would you like further details on the limit analysis or function behavior?

Here are 5 related questions:
1. What are the conditions for a function to be continuous at a point?
2. How is the limit of a function at a point defined?
3. Can you explain the difference between one-sided and two-sided limits?
4. What happens if a function has a hole or jump at a certain point?
5. How do you determine if a function is undefined at a certain point?

**Tip:** Always check for open circles or breaks in the graph to identify where the function might be undefined.

Analyze a function's graph to determine where the function is undefined, continuous, and where limits exist. This problem involves key concepts such as limits and continuity, suitable for students in Grades 10-12.

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