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
![### Evaluating Composite Functions Using Graphs
In this exercise, we will use the graphs of functions \( f \) and \( g \) to evaluate \( g(f(2)) \).
#### Graph Description:
The image includes a coordinate plane with two graphs:
1. The graph of function \( g \), a smooth curve that passes through the points \((-2, 1)\), \( (2, 4) \), and \( (4, 3) \).
2. The graph of function \( f \), a V-shaped graph that passes through the points \((2, -2)\).
The x-axis and y-axis are both clearly marked.
#### Step-by-Step Solution:
1. **Find \( f(2) \):**
- Locate \( x = 2 \) on the graph of \( f \).
- The graph of \( f \) shows that the value at \( x = 2 \) is \( f(2) = -2 \).
2. **Find \( g(f(2)) = g(-2) \):**
- Now, locate \( x = -2 \) on the graph of \( g \).
- The graph of \( g \) shows that the value at \( x = -2 \) is \( g(-2) = 1 \).
Thus, \[ g(f(2)) = g(-2) = 1 \].
#### Conclusion:
Using the graphs of the functions \( f \) and \( g \), we evaluated \( g(f(2)) \) to be 1.
#### Choices:
- \( 4 \)
- \( 2 \)
- \(-2 \)
- \( 0 \)
Based on the evaluation, the correct choice is \( 1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F779905b8-c726-43f3-8767-f38a7b511492%2Fb8024517-68e3-4f28-b429-1ead1df238f5%2Favxph2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Composite Functions Using Graphs
In this exercise, we will use the graphs of functions \( f \) and \( g \) to evaluate \( g(f(2)) \).
#### Graph Description:
The image includes a coordinate plane with two graphs:
1. The graph of function \( g \), a smooth curve that passes through the points \((-2, 1)\), \( (2, 4) \), and \( (4, 3) \).
2. The graph of function \( f \), a V-shaped graph that passes through the points \((2, -2)\).
The x-axis and y-axis are both clearly marked.
#### Step-by-Step Solution:
1. **Find \( f(2) \):**
- Locate \( x = 2 \) on the graph of \( f \).
- The graph of \( f \) shows that the value at \( x = 2 \) is \( f(2) = -2 \).
2. **Find \( g(f(2)) = g(-2) \):**
- Now, locate \( x = -2 \) on the graph of \( g \).
- The graph of \( g \) shows that the value at \( x = -2 \) is \( g(-2) = 1 \).
Thus, \[ g(f(2)) = g(-2) = 1 \].
#### Conclusion:
Using the graphs of the functions \( f \) and \( g \), we evaluated \( g(f(2)) \) to be 1.
#### Choices:
- \( 4 \)
- \( 2 \)
- \(-2 \)
- \( 0 \)
Based on the evaluation, the correct choice is \( 1 \).
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.
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