m.2 ### Piecewise Functions - Graphing Example#### Problem Statement:Sketch a graph of \( f(x) \):\[f(x) = \begin{cases} 1 & \text{if} \ x \leq -1 \\-2x - 1 & \text{if} \ -1 < x \leq 1 \\-1 & \text{if} \ x > 1 \end{cases}\]#### Graph Explanation:The given graph consists of a coordinate grid with the x-axis and y-axis both ranging from -5 to 5. The piecewise function defined above is plotted on this grid with the following details:1. **For \( x \leq -1 \)**: The function is constant at \( y = 1 \). This means for all x-values less than or equal to -1, the y-value is 1. The segment is closed and horizontal extending infinitely to the left.2. **For \( -1 < x \leq 1 \)**: The function is linear and given by \( y = -2x - 1 \). In this domain, the line starts just to the right of \( x = -1 \), where y would be slightly greater than \( y = 1 \), and continues until \( x = 1 \) (inclusive), where \( y = -3 \). The graph shows this as a diagonal line segment connecting the points that correspond to \( x = -1 \) and \( x = 1 \).3. **For \( x > 1 \)**: Again, the function is constant but this time at \( y = -1 \). This segment is horizontal and closed, extending infinitely to the right from \( x = 1 \).#### Notes:- **Open/Closed Dots**: Use open or closed dots to indicate whether the endpoints of segments are included or not. Closed dots mean that the point is included (≤ or ≥), while an open dot means that the point is not included (< or >).- **Drawing Instructions**: Click once at one end of the line segment, then move the mouse to the other endpoint and click again to draw a line segment. Click outside the graph if you need to end the line.#### Additional Resources:- For further assistance on drawing piecewise functions, refer to the following instructional videos: * [Video 1](#)

The piecewise-defined function is,We have to sketch a graph of the function.

Sketch a graph of f(z) -4-3 13 if -2z-1 if -1 z ≤-1 -1 < z <1 if z > 1 Clear All Draw: Line Dot Open Dot Notes: Only use open/closed dots if two parts of the function don't connect. To draw a line segment click once at one end, then move mouse to other end and click again. Then, click outside the graph if you need to end the line.