Sketch the graph of the piecewise function q(x) using Xy-charts. Зх + 3 ifx < -1 q(x) = { 2x + 4 if x > -1 1) Complete an Xy-chart for each piece of the given function. Be sure to use correct inputs based on the domain of each piece of the function, and use solid or open dots to denote whether a point is part of the graph or not.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please help me create an xy chart and graph the chart. 

**Sketching the Graph of a Piecewise Function**

To graph the piecewise function \( q(x) \) using XY-charts, follow these steps:

### Function Definition

The piecewise function \( q(x) \) is defined as:
\[ 
q(x) = 
\begin{cases} 
3x + 3 & \text{if } x \leq -1 \\ 
2x + 4 & \text{if } x > -1 
\end{cases} 
\]

### Instructions

1. **Complete an XY-Chart:** 
   - For each segment of the piecewise function, fill out an XY-chart.
   - Ensure the inputs (x-values) correspond to the domain of each function piece.
   - Use solid dots to represent points that are part of the graph (inclusive), and open dots for points that are not part of the graph (exclusive).

### XY-Chart Layout

- **Chart for \( 3x + 3 \):** 
  - Use values where \( x \leq -1 \).
  - Indicate solid points for these values.

- **Chart for \( 2x + 4 \):** 
  - Use values where \( x > -1 \).
  - Indicate solid points for these values.

Each chart has placeholders for \( x \) and \( y \) values, with solid dots marked to indicate included points.

### Controls
- **Add Row:** Use this to add more input points as needed.
- **Delete Row:** Use this to remove unnecessary input points.

This setup allows for a structured approach to plotting and understanding piecewise functions using XY-charts.
Transcribed Image Text:**Sketching the Graph of a Piecewise Function** To graph the piecewise function \( q(x) \) using XY-charts, follow these steps: ### Function Definition The piecewise function \( q(x) \) is defined as: \[ q(x) = \begin{cases} 3x + 3 & \text{if } x \leq -1 \\ 2x + 4 & \text{if } x > -1 \end{cases} \] ### Instructions 1. **Complete an XY-Chart:** - For each segment of the piecewise function, fill out an XY-chart. - Ensure the inputs (x-values) correspond to the domain of each function piece. - Use solid dots to represent points that are part of the graph (inclusive), and open dots for points that are not part of the graph (exclusive). ### XY-Chart Layout - **Chart for \( 3x + 3 \):** - Use values where \( x \leq -1 \). - Indicate solid points for these values. - **Chart for \( 2x + 4 \):** - Use values where \( x > -1 \). - Indicate solid points for these values. Each chart has placeholders for \( x \) and \( y \) values, with solid dots marked to indicate included points. ### Controls - **Add Row:** Use this to add more input points as needed. - **Delete Row:** Use this to remove unnecessary input points. This setup allows for a structured approach to plotting and understanding piecewise functions using XY-charts.
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