**Task:** Express the function graphed on the axes below as a piecewise function. **Graph Explanation:** The graph depicts a piecewise function with two linear segments. It consists of a vertical axis labeled \( y \) and a horizontal axis labeled \( x \). 1. **Left Segment (from \( x = -8 \) to \( x = 0 \)):** - This segment is defined for \( x \leq 0 \). - The line connects the points \((-8, 8)\) and \((0, 4)\). - It is a descending line. 2. **Right Segment (from \( x = 0 \) to \( x = 6 \)):** - This segment is defined for \( 0 < x \leq 6 \). - The line connects the points \((0, 4)\) and \((6, 8)\). - It is an ascending line. **Answer Form Section:** - There are two input boxes for defining the piecewise function. - The function \( f(x) \) is divided into sections using braces, with empty boxes provided to fill in the equations and constraints for each piece of the function. - Buttons below allow for specifying inequalities (e.g., \( < \), \( \leq \), \( > \), \( \geq \), and \( \neq \)). **Function Input Example:** - \( f(x) = -\frac{1}{2}x + 4 \quad \text{for} \quad x \leq 0 \) - \( f(x) = \frac{2}{3}x + 4 \quad \text{for} \quad 0 < x \leq 6 \) **Actions:** - "Add Rule" and "Remove Rule" buttons are available for managing the function rules. - A "Submit Answer" button is provided to submit the completed function.
**Task:** Express the function graphed on the axes below as a piecewise function. **Graph Explanation:** The graph depicts a piecewise function with two linear segments. It consists of a vertical axis labeled \( y \) and a horizontal axis labeled \( x \). 1. **Left Segment (from \( x = -8 \) to \( x = 0 \)):** - This segment is defined for \( x \leq 0 \). - The line connects the points \((-8, 8)\) and \((0, 4)\). - It is a descending line. 2. **Right Segment (from \( x = 0 \) to \( x = 6 \)):** - This segment is defined for \( 0 < x \leq 6 \). - The line connects the points \((0, 4)\) and \((6, 8)\). - It is an ascending line. **Answer Form Section:** - There are two input boxes for defining the piecewise function. - The function \( f(x) \) is divided into sections using braces, with empty boxes provided to fill in the equations and constraints for each piece of the function. - Buttons below allow for specifying inequalities (e.g., \( < \), \( \leq \), \( > \), \( \geq \), and \( \neq \)). **Function Input Example:** - \( f(x) = -\frac{1}{2}x + 4 \quad \text{for} \quad x \leq 0 \) - \( f(x) = \frac{2}{3}x + 4 \quad \text{for} \quad 0 < x \leq 6 \) **Actions:** - "Add Rule" and "Remove Rule" buttons are available for managing the function rules. - A "Submit Answer" button is provided to submit the completed function.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Task:** Express the function graphed on the axes below as a piecewise function.
**Graph Explanation:**
The graph depicts a piecewise function with two linear segments. It consists of a vertical axis labeled \( y \) and a horizontal axis labeled \( x \).
1. **Left Segment (from \( x = -8 \) to \( x = 0 \)):**
- This segment is defined for \( x \leq 0 \).
- The line connects the points \((-8, 8)\) and \((0, 4)\).
- It is a descending line.
2. **Right Segment (from \( x = 0 \) to \( x = 6 \)):**
- This segment is defined for \( 0 < x \leq 6 \).
- The line connects the points \((0, 4)\) and \((6, 8)\).
- It is an ascending line.
**Answer Form Section:**
- There are two input boxes for defining the piecewise function.
- The function \( f(x) \) is divided into sections using braces, with empty boxes provided to fill in the equations and constraints for each piece of the function.
- Buttons below allow for specifying inequalities (e.g., \( < \), \( \leq \), \( > \), \( \geq \), and \( \neq \)).
**Function Input Example:**
- \( f(x) = -\frac{1}{2}x + 4 \quad \text{for} \quad x \leq 0 \)
- \( f(x) = \frac{2}{3}x + 4 \quad \text{for} \quad 0 < x \leq 6 \)
**Actions:**
- "Add Rule" and "Remove Rule" buttons are available for managing the function rules.
- A "Submit Answer" button is provided to submit the completed function.
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