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From the graph, we need to find the value of \( f(-1) \).

Looking at the function graph, \( f(-1) \) corresponds to the value of the function at \( x = -1 \). The graph shows that at \( x = -1 \), the function has a point of discontinuity, with two different values approaching from the left and right.

The left-side limit as \( x \) approaches \( -1 \) is \( 3 \), and the right-side limit as \( x \) approaches \( -1 \) is \( 1 \), as indicated in your results for the limits. However, the function itself appears not to be defined at \( x = -1 \) as the overall limit does not exist and there's a visible gap at \( x = -1 \).

Therefore, \( f(-1) \) is not defined (DNE) due to this discontinuity at \( x = -1 \).

Would you like to know more details or have any other questions? Here are a few follow-up topics you might consider:

1. What causes a function to have a discontinuity?
2. How do we calculate limits from a graph?
3. What are the different types of discontinuities?
4. Can a function have a limit at a point where it is not defined?
5. How to find the equation of a piecewise function from a graph?

**Tip:** When checking for function values or limits from a graph, always confirm if the point is included (filled circle) or excluded (open circle) as it significantly affects the interpretation.

Find the limit and function value for f(x) as x approaches -1 based on the given graph.

Explore the limit behavior and discontinuity of the function f(x) at x = -1. This problem highlights key concepts in calculus, such as left-hand and right-hand limits, and understanding discontinuities. Suitable for students in Grades 10-12.

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