https://file.aiquickdraw.com/mathbot/file/1726851141865hyr7yx0a.jpg

Here's the graph of the given piecewise function \( f(x) \):

1. The blue line represents the linear segment \( f(x) = -\frac{1}{3}x + 3 \) for \( -6 \leq x \leq -3 \).
   - The filled blue circle at \( x = -3 \) indicates the endpoint where the first piece ends.

2. The green horizontal line represents the constant value \( f(x) = 4 \) for \( -3 < x < 5 \).
   - The open green circle at \( x = -3 \) indicates a discontinuity, showing that \( f(x) \) is not defined as 4 at \( x = -3 \), but immediately jumps from 3 to 4 after this point.

Would you like more details on the graph or any clarifications?

Here are some related questions for further exploration:
1. How do you find the slope of a line from its equation?
2. How does the graph of a constant function look like, and why?
3. What happens when there is a discontinuity in a piecewise function?
4. How would you graph a quadratic function as part of a piecewise function?
5. What are the conditions for a function to be continuous at a given point?

**Tip**: Always look at endpoints carefully when graphing piecewise functions. Some are included (closed circle), while others are not (open circle).

Graph the piecewise function f(x) where f(x) = -1/3x + 3 for -6 <= x <= -3 and f(x) = 4 for -3 < x < 5.

Learn how to graph a piecewise function that includes a linear segment and a constant function. This example covers the function f(x), where f(x) = -1/3x + 3 for -6 <= x <= -3 and f(x) = 4 for -3 < x < 5. The problem also highlights discontinuities in piecewise graphs.

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