https://file.aiquickdraw.com/mathbot/file/1725587586863tel12jdo.jpg

Let's analyze the problem step-by-step based on the graphs and the requested function values and limits:

We have two graphs: Graph A and Graph B. The task asks to evaluate the following expressions using the graphs:

### 1. \( f(3) \)
   - From **Graph A** and **Graph B**:
     - Look at the y-coordinate where \( x = 3 \).

### 2. \( \lim_{x \to 3} f(x) \)
   - Check the limit of the function as \( x \) approaches 3.
   - Does the function approach a particular value from both sides?

### 3. \( f(-3) \)
   - Evaluate the function at \( x = -3 \).
   
### 4. \( \lim_{x \to -3} f(x) \)
   - Find the value the function approaches as \( x \) gets close to -3 from both sides.

### Graph A Analysis:
- Graph A seems to have a piecewise function with a possible jump discontinuity.
- From **Graph A**, when \( x = 3 \), the point on the graph is an open circle (so \( f(3) \) might be undefined). However, for the limit \( \lim_{x \to 3} f(x) \), it looks like the y-value approaches some value.
- The same logic applies to \( x = -3 \).

### Graph B Analysis:
- Similar observations need to be made for Graph B by looking at where \( x = 3 \) and \( x = -3 \).

Let me interpret the graph values for these specific points.

I have opened the image, allowing me to examine it closely. I'll now interpret the values for \( f(3) \), \( f(-3) \), and the corresponding limits using both graphs.

### Graph A:
1. **For \( f(3) \)**:
   - The point at \( x = 3 \) appears to have an open circle, indicating that the function is undefined at \( x = 3 \). Thus, \( f(3) \) in **Graph A** is undefined.

2. **For \( \lim_{x \to 3} f(x) \)**:
   - The graph seems to approach a certain value as \( x \) approaches 3 from both sides. It looks like the graph approaches \( y = 2 \), so the limit is likely \( 2 \).

3. **For \( f(-3) \)**:
   - The graph has a defined point at \( x = -3 \) (likely a filled point), meaning \( f(-3) \) should be the y-coordinate at that point, which is \( f(-3) = 1 \).

4. **For \( \lim_{x \to -3} f(x) \)**:
   - As \( x \) approaches -3, the graph seems to be approaching \( y = 1 \) from both sides, so the limit is \( 1 \).

### Graph B:
1. **For \( f(3) \)**:
   - Similar to Graph A, \( x = 3 \) seems to have a value at \( y = 1 \). Thus, \( f(3) = 1 \) in Graph B.

2. **For \( \lim_{x \to 3} f(x) \)**:
   - The limit as \( x \) approaches 3 appears to be \( 1 \), as the graph approaches this value from both sides.

3. **For \( f(-3) \)**:
   - The point at \( x = -3 \) has a value of \( f(-3) = -1 \).

4. **For \( \lim_{x \to -3} f(x) \)**:
   - The limit as \( x \) approaches -3 is \( -1 \), as the graph tends to this value from both sides.

### Final Results:
- **Graph A:**
  - \( f(3) \) is undefined.
  - \( \lim_{x \to 3} f(x) = 2 \).
  - \( f(-3) = 1 \).
  - \( \lim_{x \to -3} f(x) = 1 \).

- **Graph B:**
  - \( f(3) = 1 \).
  - \( \lim_{x \to 3} f(x) = 1 \).
  - \( f(-3) = -1 \).
  - \( \lim_{x \to -3} f(x) = -1 \).

Would you like further details or explanations on these results?

Here are 5 related questions to explore further:
1. How do we determine limits graphically?
2. What is the difference between a limit and the value of a function?
3. What are jump discontinuities, and how do they affect limits?
4. How can we distinguish between open and closed points on graphs?
5. What are the formal definitions of left-hand and right-hand limits?

**Tip:** When checking limits graphically, always observe the trend of the graph from both the left and right sides as \( x \) approaches the point of interest.

Learn how to analyze and evaluate limits and function values using graphs. This problem involves concepts like limits, continuity, and piecewise functions, and uses the limit definition and laws to find the function's behavior at specific points. Suitable for students in Grades 10-12.

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