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.