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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![### 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 \( 1 \).
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