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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What is the range
![### Piecewise Functions
In Chapter 1, Sections 1.1, 1.2, and 1.3, we explore the topic of piecewise functions. Here, we are given a specific piecewise function defined over the domain \((-∞, ∞)\):
\[ f(x) = \begin{cases}
x + 4 & \text{if } x < -1 \\
x - 4 & \text{if } x \geq -1
\end{cases} \]
This function has two different expressions based on the value of \(x\):
- **For \(x\) less than -1:** The function is defined as \(f(x) = x + 4\).
- **For \(x\) greater than or equal to -1:** The function is defined as \(f(x) = x - 4\).
Below the function, a portion of the image shows a plot, which is partially visible. The graph appears to host two linear segments that match the given conditions. The diagram includes the y-axis and the x-axis, and the grid points are marked. The y-axis and x-axis are labeled. Values on the axes are distinctly plotted at each interval.
The question below the graph (marked as "B.") seems to be part of a multiple-choice question, aiming to verify understanding or interpretation of the piecewise function and its graphical representation. Note that the full detail of the graph and the question options is not given in the image.
### Key Points to Note:
- Understanding piecewise functions involves recognizing different rules for different intervals of the domain.
- Practicing graphing piecewise functions helps in visualizing how these functions behave across their distinct domains.
This will aid in strengthening your grasp on how to handle and interpret piecewise functions in various mathematical scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2107c9d4-03cf-46c4-aa9a-f455311ac0bc%2Ff15479c5-7abf-4199-9cb1-2f5010b1b2fb%2F3i0yzzj_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Piecewise Functions
In Chapter 1, Sections 1.1, 1.2, and 1.3, we explore the topic of piecewise functions. Here, we are given a specific piecewise function defined over the domain \((-∞, ∞)\):
\[ f(x) = \begin{cases}
x + 4 & \text{if } x < -1 \\
x - 4 & \text{if } x \geq -1
\end{cases} \]
This function has two different expressions based on the value of \(x\):
- **For \(x\) less than -1:** The function is defined as \(f(x) = x + 4\).
- **For \(x\) greater than or equal to -1:** The function is defined as \(f(x) = x - 4\).
Below the function, a portion of the image shows a plot, which is partially visible. The graph appears to host two linear segments that match the given conditions. The diagram includes the y-axis and the x-axis, and the grid points are marked. The y-axis and x-axis are labeled. Values on the axes are distinctly plotted at each interval.
The question below the graph (marked as "B.") seems to be part of a multiple-choice question, aiming to verify understanding or interpretation of the piecewise function and its graphical representation. Note that the full detail of the graph and the question options is not given in the image.
### Key Points to Note:
- Understanding piecewise functions involves recognizing different rules for different intervals of the domain.
- Practicing graphing piecewise functions helps in visualizing how these functions behave across their distinct domains.
This will aid in strengthening your grasp on how to handle and interpret piecewise functions in various mathematical scenarios.
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