https://file.aiquickdraw.com/mathbot/file/1726314856027rlt52vfo.jpg

I have displayed the image you uploaded. Let's proceed by interpreting the conditions stated to sketch the graph.

The question specifies the following:
- \( f(0) = -1 \)
- \( f(3) = 1 \)
- \( \lim_{x \to 0} f(x) = 1 \)
- \( \lim_{x \to 3^-} f(x) = -2 \)
- \( \lim_{x \to 3^+} f(x) = 2 \)

### Steps to Draw the Graph:
1. **At \( x = 0 \)**, \( f(0) = -1 \): There will be a point at \( (0, -1) \).
2. **At \( x = 3 \)**, \( f(3) = 1 \): Another point will be at \( (3, 1) \).
3. **As \( x \) approaches 0 from both sides**, \( \lim_{x \to 0} f(x) = 1 \): This suggests that the function tends toward \( y = 1 \) near \( x = 0 \), but there’s a discontinuity at \( x = 0 \) where the actual value is \( -1 \).
4. **As \( x \to 3^- \)**, \( \lim_{x \to 3^-} f(x) = -2 \): This means that approaching \( x = 3 \) from the left, the graph approaches \( y = -2 \).
5. **As \( x \to 3^+ \)**, \( \lim_{x \to 3^+} f(x) = 2 \): As \( x = 3 \) is approached from the right, the graph tends to \( y = 2 \).

I'll sketch the graph now based on these details.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you'd like, I can guide you step-by-step on how to sketch the graph manually, or we can attempt another approach. Let me know how you'd like to proceed! 

In the meantime, here are five related questions you might find interesting:
1. What does it mean when a limit differs from the function's value at a point?
2. How does left-hand and right-hand limits affect continuity?
3. What kinds of discontinuities can appear in functions?
4. How would you adjust the graph if the limits as \( x \to 3^- \) and \( x \to 3^+ \) were the same?
5. How can we determine if a function is continuous or piecewise based on given conditions?

**Tip:** When drawing graphs, always check for key points (e.g., function values) and limit behavior to ensure you capture discontinuities correctly.

A graph that contains: (a) f(0) = -1, (b) f(3) = 1, (c) lim(x→0) f(x) = 1, (d) lim(x→3-) f(x) = -2, (e) lim(x→3+) f(x) = 2

Explore a detailed solution to a problem involving function values and limits. Learn how to graph a function with discontinuities at specific points such as f(0) = -1, f(3) = 1, and limits lim(x→0), lim(x→3-), and lim(x→3+). Suitable for advanced high school students (Grades 11-12).

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