https://file.aiquickdraw.com/mathbot/file/1726668244558w7praeh3.jpg

The image shows a problem involving limits, specifically:

1. \( \lim\limits_{x \to a^-} f(x) \)
2. \( \lim\limits_{x \to a^+} f(x) \)
3. \( \lim\limits_{x \to a} f(x) \)
4. \( f(a) \) (if it exists).

The graph has arrows indicating behavior as \( x \to 3^- \) and \( x \to 3^+ \), with \( f(3) \) and \( f(4) \) also potentially relevant. The first part has already been answered: \( \lim\limits_{x \to 3^-} f(x) = 3 \).

For the second part:

### \( \lim\limits_{x \to 3^+} f(x) \)
From the graph:
- As \( x \to 3^+ \), the graph approaches the value \( 1 \).

So, \( \lim\limits_{x \to 3^+} f(x) = 1 \).

Let me know if you'd like further details or clarification!

Here are some related questions to consider:

1. What is \( \lim\limits_{x \to 4^-} f(x) \)?
2. What is \( f(3) \)?
3. How does the continuity of \( f(x) \) change at \( x = 3 \)?
4. Does the limit at \( x = 1 \) exist?
5. Can you determine \( f(2) \) from the graph?

### Tip:
For a limit to exist at \( x = a \), both the left-hand limit and right-hand limit must be equal and finite.

Find the limits and function values for f(x) at x approaching 3 and 1.

Explore how to analyze limits and evaluate function values at specific points using a piecewise function graph. This tutorial includes understanding limits from the left and right, and assessing function continuity.

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