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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![# Using the Graph of y = f(x) to Answer Questions
## Objective:
Determine the values of \( x \) for which \( f(x) \leq 0 \) using the provided graph of the function \( y = f(x) \).
## Graph Description:
- The graph depicts the function \( y = f(x) \) in red.
- The x-axis and y-axis range from -16 to 16 and -6 to 6, respectively.
- Various key points are marked on the graph with coordinates labeled, including intercepts and critical points.
### Key Points on the Graph:
- Intercept Points:
- \( ( \frac{-23}{2}, 0 ) \)
- \( ( -8, 0 ) \)
- \( (1, 0 ) \)
- \( (3, 2 ) \)
- Critical Points:
- \( ( -10, 3 ) \)
- \( ( -12, -3 ) \)
- \( ( -6, -5 ) \)
- \( ( -3, -1 ) \)
- \( ( -4, -3 ) \)
- \( (0, -1) \)
- \( (5, 0) \)
### Explanation of the Graph:
- The function \( y = f(x) \) crosses the x-axis at four points, indicating that these are the roots of the function: \( x = \frac{-23}{2} \), \( x = -8 \), \( x = 1 \), and \( x = 5 \).
- The function takes both positive and negative values along its course, crossing the x-axis multiple times.
## Analysis:
- To determine where \( f(x) \leq 0 \):
- The function is less than or equal to zero in the intervals where the graph is at or below the x-axis.
- Based on the graph:
1. For \( x \in [ -\infty, \frac{-23}{2} ] \), the function \( f(x) \leq 0 \).
2. For \( x \in [ -8, 1 ] \), the function \( f(x) \leq 0 \).
## Conclusion:
The values of \( x \) for which \( f(x) \leq 0 \) are:
\[ x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5c1f0d4-7408-4361-a2b7-403007286980%2F9d33d680-204c-4dbc-895e-97b2b059e2f1%2Ftgjlt44_processed.png&w=3840&q=75)
Transcribed Image Text:# Using the Graph of y = f(x) to Answer Questions
## Objective:
Determine the values of \( x \) for which \( f(x) \leq 0 \) using the provided graph of the function \( y = f(x) \).
## Graph Description:
- The graph depicts the function \( y = f(x) \) in red.
- The x-axis and y-axis range from -16 to 16 and -6 to 6, respectively.
- Various key points are marked on the graph with coordinates labeled, including intercepts and critical points.
### Key Points on the Graph:
- Intercept Points:
- \( ( \frac{-23}{2}, 0 ) \)
- \( ( -8, 0 ) \)
- \( (1, 0 ) \)
- \( (3, 2 ) \)
- Critical Points:
- \( ( -10, 3 ) \)
- \( ( -12, -3 ) \)
- \( ( -6, -5 ) \)
- \( ( -3, -1 ) \)
- \( ( -4, -3 ) \)
- \( (0, -1) \)
- \( (5, 0) \)
### Explanation of the Graph:
- The function \( y = f(x) \) crosses the x-axis at four points, indicating that these are the roots of the function: \( x = \frac{-23}{2} \), \( x = -8 \), \( x = 1 \), and \( x = 5 \).
- The function takes both positive and negative values along its course, crossing the x-axis multiple times.
## Analysis:
- To determine where \( f(x) \leq 0 \):
- The function is less than or equal to zero in the intervals where the graph is at or below the x-axis.
- Based on the graph:
1. For \( x \in [ -\infty, \frac{-23}{2} ] \), the function \( f(x) \leq 0 \).
2. For \( x \in [ -8, 1 ] \), the function \( f(x) \leq 0 \).
## Conclusion:
The values of \( x \) for which \( f(x) \leq 0 \) are:
\[ x
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