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...
Related questions
Question
Classify the type of discontinuity manifested by the function
![### Piecewise Function
Consider the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
x^2 + 2 & \text{for } x \leq 0 \\
1 & \text{for } x > 0
\end{cases}
\]
Here is a breakdown of the function:
1. **For \( x \leq 0 \)**:
- The function \( f(x) \) is given by \( x^2 + 2 \).
- This represents a quadratic function (a parabola) shifted up by 2 units.
2. **For \( x > 0 \)**:
- The function \( f(x) \) is constant and equals 1.
### Explanation
This piecewise function consists of two parts:
- The first part applies when \( x \) is less than or equal to zero. In this region, the function outputs values from a parabolic curve.
- The second part applies when \( x \) is greater than zero. Here, the function outputs a constant value of 1 regardless of \( x \).
### Graphical Representation
- **For \( x \leq 0 \)**: The graph would be a parabola opening upwards with its vertex at the point (0, 2).
- **For \( x > 0 \)**: The graph would be a flat line (horizontal) at \( y = 1 \).
Understanding and analyzing piecewise functions like this is important in various fields of mathematics and applied sciences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa44093f9-865e-42e2-9761-7238b47b32ab%2Fc959096e-095f-4c8c-9135-8f415e65b416%2F4h8oqyb_processed.png&w=3840&q=75)
Transcribed Image Text:### Piecewise Function
Consider the piecewise function \( f(x) \) defined as follows:
\[
f(x) =
\begin{cases}
x^2 + 2 & \text{for } x \leq 0 \\
1 & \text{for } x > 0
\end{cases}
\]
Here is a breakdown of the function:
1. **For \( x \leq 0 \)**:
- The function \( f(x) \) is given by \( x^2 + 2 \).
- This represents a quadratic function (a parabola) shifted up by 2 units.
2. **For \( x > 0 \)**:
- The function \( f(x) \) is constant and equals 1.
### Explanation
This piecewise function consists of two parts:
- The first part applies when \( x \) is less than or equal to zero. In this region, the function outputs values from a parabolic curve.
- The second part applies when \( x \) is greater than zero. Here, the function outputs a constant value of 1 regardless of \( x \).
### Graphical Representation
- **For \( x \leq 0 \)**: The graph would be a parabola opening upwards with its vertex at the point (0, 2).
- **For \( x > 0 \)**: The graph would be a flat line (horizontal) at \( y = 1 \).
Understanding and analyzing piecewise functions like this is important in various fields of mathematics and applied sciences.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning