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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![### Graph Analysis and Function Description
#### Image Description:
This image shows a section of a math worksheet containing a graph and a piecewise function. The graph is a standard Cartesian coordinate system grid with x and y axes labeled from -6 to 6 on both axes.
#### Function:
The function \( h(x) \) is defined as a piecewise function:
\[
h(x) =
\begin{cases}
\sqrt[3]{x} & \text{if } x \leq -1 \\
x & \text{if } -1 < x \leq 1 \\
-\sqrt{x} & \text{if } x > 1
\end{cases}
\]
**Domain and Range:**
- **Domain:** Not explicitly given, but can be inferred from the piecewise conditions.
- **Range:** Not specified; needs calculation or graph inspection.
**Function Values:**
These need to be calculated based on the function definition:
- \( h(-8) = \)
- \( h(0) = \)
- \( h(4) = \)
#### Graph:
- The graph is divided into quadrants by the x and y axes.
- Use the piecewise rules to plot the function across the relevant sections.
This content is suitable for a mathematics lesson focused on understanding and interpreting piecewise functions, as well as practicing graphing skills.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F629c87a2-ae5f-4a64-87c9-a8c68753814a%2F91dd57b5-4bf1-4df1-8edc-404304bbb324%2F39bt5a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graph Analysis and Function Description
#### Image Description:
This image shows a section of a math worksheet containing a graph and a piecewise function. The graph is a standard Cartesian coordinate system grid with x and y axes labeled from -6 to 6 on both axes.
#### Function:
The function \( h(x) \) is defined as a piecewise function:
\[
h(x) =
\begin{cases}
\sqrt[3]{x} & \text{if } x \leq -1 \\
x & \text{if } -1 < x \leq 1 \\
-\sqrt{x} & \text{if } x > 1
\end{cases}
\]
**Domain and Range:**
- **Domain:** Not explicitly given, but can be inferred from the piecewise conditions.
- **Range:** Not specified; needs calculation or graph inspection.
**Function Values:**
These need to be calculated based on the function definition:
- \( h(-8) = \)
- \( h(0) = \)
- \( h(4) = \)
#### Graph:
- The graph is divided into quadrants by the x and y axes.
- Use the piecewise rules to plot the function across the relevant sections.
This content is suitable for a mathematics lesson focused on understanding and interpreting piecewise functions, as well as practicing graphing skills.
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