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Here is the graph of the piecewise function \( f(x) \) based on the provided conditions. The graph shows the three segments of the function:

1. A horizontal line at \( y = 1 \) for \( x \leq -1 \).
2. A line segment from \( (-1, -1) \) to \( (2, -5) \).
3. A horizontal line at \( y = -3 \) for \( x > 2 \).

Please let me know if you need any more details or have any questions.

### Follow-up Questions:

1. What are the values of \( f(x) \) at the boundary points \( x = -1 \) and \( x = 2 \)?
2. How would the graph change if the condition \( x > 2 \) changed to \( x \geq 2 \)?
3. What is the domain and range of the given piecewise function?
4. How can we find the slope of the line segment for \( -1 < x \leq 2 \)?
5. What is the significance of open and closed dots in a graph of a piecewise function?

### Tip:
When graphing piecewise functions, always carefully check the domain of each piece and use open or closed dots to denote whether a point is included in the segment.

Sketch a graph of f(x) = {1 if x <= -1, -2x - 1 if -1 < x <= 2, -3 if x > 2}

Learn how to graph a piecewise function with three conditions: a constant for x ≤ -1, a linear segment for -1 < x ≤ 2, and another constant for x > 2. This problem involves understanding the nature of piecewise functions and graphing them accurately on the coordinate plane.

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