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.