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The graph shows the distance, in miles, Keandra traveled from her home over a certain amount of time, in minutes.



graph with the x axis labeled time in minutes and the y axis labeled distance in miles, with a line segment from 0 comma 0 to 40 comma 100, a horizontal line segment from 40 comma 100 to 80 comma 100, a line segment from 80 comma 100 to 100 comma 125 and a line segment from 100 comma 125 to 120 comma 100

Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant. (2 points)

Part B: Write a detailed description for the graph using information from Part A. (2 points)

1 answer

Part A: Identify the intervals

  1. Increasing: The graph is increasing in the interval from \( (0, 0) \) to \( (40, 100) \), corresponding to the time interval from 0 to 40 minutes. During this time, Keandra's distance from home increases from 0 miles to 100 miles.

  2. Constant: The graph is constant in the interval from \( (40, 100) \) to \( (80, 100) \). During this time, the distance remains at 100 miles for 40 minutes (from 40 to 80 minutes).

  3. Increasing: The graph increases again in the interval from \( (80, 100) \) to \( (100, 125) \). During this time, Keandra travels from 100 miles to 125 miles over the time interval from 80 to 100 minutes.

  4. Decreasing: The graph is decreasing in the interval from \( (100, 125) \) to \( (120, 100) \). During this time, Keandra's distance decreases from 125 miles to 100 miles over the final 20 minutes (from 100 to 120 minutes).

Summary of intervals:

  • Increasing: \( (0, 40) \) and \( (80, 100) \)
  • Constant: \( (40, 80) \)
  • Decreasing: \( (100, 120) \)

Part B: Detailed Description of the Graph

The graph depicts Keandra's journey over a period of 120 minutes, illustrating her distance from home in miles. Initially, from 0 to 40 minutes, her distance increases steadily from 0 to 100 miles, indicating that she is traveling away from home at a consistent rate. After 40 minutes, Keandra maintains a constant distance of 100 miles from home for the next 40 minutes (from 40 to 80 minutes), suggesting that she may have stopped or reached a destination without traveling further.

Following this period of constancy, Keandra resumes her journey, increasing her distance from 100 miles to 125 miles between 80 and 100 minutes, showing a renewed rate of travel. However, after 100 minutes, the trend shifts as her distance begins to decrease, dropping from 125 miles back to 100 miles over the final 20 minutes (from 100 to 120 minutes). This decline indicates that Keandra is likely returning towards home, concluding her journey at 120 minutes. Throughout the journey, the graph effectively illustrates periods of motion, rest, and the eventual return, allowing for a comprehensive understanding of Keandra's travel.