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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Question
![**Title: Understanding Absolute Value Functions**
**Objective: Find the formula for the function whose graph is the given curve.**
**Graph Analysis:**
The graph displays a V-shaped curve that indicates an absolute value function.
- The x-axis is labeled from -8 to 8.
- The y-axis ranges from -15 to 15.
The function graph is represented by two linear segments:
1. The left segment decreases from the point (0, -8) to (-4, 0).
2. The right segment increases from the point (0, -8) to (4, 0).
**Function Formula Box:**
There is a formula input box which shows:
\[ y = -|x| \]
This formula describes the transformation applied to the basic absolute value function \( y = |x| \). The negative sign reflects the graph vertically, creating a V-shape with the vertex at the point (0, -8).
**Additional Resources:**
- A button labeled "Need help?" followed by "Show me" suggests guidance or hints for finding the correct formula.
This interactive element allows users to experiment with entering and adjusting the formula to match the graph accurately.
**Closing Note:**
Understanding how transformations affect the graph of an absolute value function allows us to model real-world situations and appreciate the geometric properties of functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa14c6553-ea6f-4133-9ef0-4acc912f2a4a%2Fb9c061fe-9350-455b-b2fd-c5e4d537ee2b%2Fyji6twq_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Absolute Value Functions**
**Objective: Find the formula for the function whose graph is the given curve.**
**Graph Analysis:**
The graph displays a V-shaped curve that indicates an absolute value function.
- The x-axis is labeled from -8 to 8.
- The y-axis ranges from -15 to 15.
The function graph is represented by two linear segments:
1. The left segment decreases from the point (0, -8) to (-4, 0).
2. The right segment increases from the point (0, -8) to (4, 0).
**Function Formula Box:**
There is a formula input box which shows:
\[ y = -|x| \]
This formula describes the transformation applied to the basic absolute value function \( y = |x| \). The negative sign reflects the graph vertically, creating a V-shape with the vertex at the point (0, -8).
**Additional Resources:**
- A button labeled "Need help?" followed by "Show me" suggests guidance or hints for finding the correct formula.
This interactive element allows users to experiment with entering and adjusting the formula to match the graph accurately.
**Closing Note:**
Understanding how transformations affect the graph of an absolute value function allows us to model real-world situations and appreciate the geometric properties of functions.
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