https://file.aiquickdraw.com/mathbot/file/1730579687397rfu84dgz.jpg

Let's analyze and solve the limits based on the provided graph for each part (a) through (c):

1. **Part (a)**: \(\lim_{{x \to 4}} f(x)\)
   - Observing the graph at \(x = 4\), we should look at the behavior of \(f(x)\) as \(x\) approaches 4 from both the left and the right.
   - The values appear to approach a specific point from both sides. Based on the options provided, it seems that the correct choice should be identified based on what we see on the graph.

2. **Part (b)**: \(\lim_{{x \to -3^+}} f(x)\)
   - This denotes the **right-hand limit** as \(x\) approaches -3 from the positive (right) side.
   - Observing the function's behavior from the right of \(x = -3\), we determine whether the function value approaches -5 or another value.

3. **Part (c)**: \(\lim_{{x \to -3^-}} f(x)\)
   - This denotes the **left-hand limit** as \(x\) approaches -3 from the negative (left) side.
   - Observing the function's behavior from the left of \(x = -3\), we determine whether there is a specific value for the limit.

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### Solutions
Let’s go through each part based on these observations from the graph:

- **(a)** Select the correct choice for \(\lim_{{x \to 4}} f(x)\) and input the answer within the choice.
- **(b)** Write the value of \(\lim_{{x \to -3^+}} f(x)\).
- **(c)** Write the value of \(\lim_{{x \to -3^-}} f(x)\).

Would you like further guidance on interpreting the graph for these values? Let me know if you'd like a detailed explanation of each limit.

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Here are some related questions to deepen your understanding:
1. What is the difference between right-hand and left-hand limits?
2. How do you determine if a two-sided limit exists based on a graph?
3. What does it mean when a function has a jump discontinuity at a point?
4. How can you determine if a function is continuous at a specific point?
5. Why do limits approaching from different directions sometimes have different values?

**Tip:** Always check the graph's behavior on both sides of the point for a limit. A two-sided limit only exists if both one-sided limits are equal.

Using the following graph of the function f, evaluate the limits (a) through (c):
(a) Select the correct choice below and fill in the answer box within the choice for lim x→4 f(x).
(b) lim x→−3⁺ f(x) = ?
(c) lim x→−3⁻ f(x) = ?

Learn how to evaluate limits using a function graph. This problem covers the concepts of right-hand and left-hand limits, helping students determine limits from graphical behavior at specified points. Suitable for high school students studying calculus or precalculus.

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