Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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
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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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