Question
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 50, a horizontal line segment from 40 comma 50 to 60 comma 50, a line segment from 60 comma 50 to 80 comma 100 and a line segment from 80 comma 100 to 120 comma 50
Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant.
Part B: Write a detailed description for the graph using information from Part A.
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 50, a horizontal line segment from 40 comma 50 to 60 comma 50, a line segment from 60 comma 50 to 80 comma 100 and a line segment from 80 comma 100 to 120 comma 50
Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant.
Part B: Write a detailed description for the graph using information from Part A.
Answers
GPT-4o mini
### Part A: Identify the Intervals
**Increasing Interval:**
- The graph is increasing between \(0\) minutes and \(40\) minutes (from \((0, 0)\) to \((40, 50)\)).
- The graph is also increasing between \(60\) minutes and \(80\) minutes (from \((60, 50)\) to \((80, 100)\)).
**Decreasing Interval:**
- There is no interval in which the graph is decreasing.
**Constant Interval:**
- The graph is constant between \(40\) minutes and \(60\) minutes (from \((40, 50)\) to \((60, 50)\)).
- The graph is also constant between \(80\) minutes and \(120\) minutes (from \((80, 100)\) to \((120, 50)\)).
### Summary of Intervals:
- **Increasing:** \(0\) to \(40\) minutes; \(60\) to \(80\) minutes
- **Decreasing:** None
- **Constant:** \(40\) to \(60\) minutes; \(80\) to \(120\) minutes
---
### Part B: Detailed Description of the Graph
The graph represents the distance Keandra traveled from her home over time in minutes.
Initially, from \(0\) to \(40\) minutes, Keandra's distance increases steadily from \(0\) miles to \(50\) miles. This increase indicates active travel during this time period.
After reaching \(50\) miles at \(40\) minutes, Keandra maintains this distance for \(20\) minutes, from \(40\) to \(60\) minutes. This flat, horizontal line signifies that she has paused or is stationary, and her distance from home does not change during this interval.
Once she resumes traveling at \(60\) minutes, her distance increases again, rising from \(50\) miles to \(100\) miles by \(80\) minutes. This demonstrates another phase of active traveling as she covers an additional \(50\) miles.
Finally, from \(80\) minutes to \(120\) minutes, the graph shows a significant decrease in distance, falling back to \(50\) miles. This leads to a second horizontal line that indicates Keandra is once again at a stationary point, remaining at \(50\) miles for \(40\) minutes.
In summary, Keandra's journey can be segmented into phases of increasing travel, periods of constant distance, and no average decrease during the observed time frame. The intervals collectively outline her movement pattern and suggest a structured journey that involves both travel and periods of rest.
**Increasing Interval:**
- The graph is increasing between \(0\) minutes and \(40\) minutes (from \((0, 0)\) to \((40, 50)\)).
- The graph is also increasing between \(60\) minutes and \(80\) minutes (from \((60, 50)\) to \((80, 100)\)).
**Decreasing Interval:**
- There is no interval in which the graph is decreasing.
**Constant Interval:**
- The graph is constant between \(40\) minutes and \(60\) minutes (from \((40, 50)\) to \((60, 50)\)).
- The graph is also constant between \(80\) minutes and \(120\) minutes (from \((80, 100)\) to \((120, 50)\)).
### Summary of Intervals:
- **Increasing:** \(0\) to \(40\) minutes; \(60\) to \(80\) minutes
- **Decreasing:** None
- **Constant:** \(40\) to \(60\) minutes; \(80\) to \(120\) minutes
---
### Part B: Detailed Description of the Graph
The graph represents the distance Keandra traveled from her home over time in minutes.
Initially, from \(0\) to \(40\) minutes, Keandra's distance increases steadily from \(0\) miles to \(50\) miles. This increase indicates active travel during this time period.
After reaching \(50\) miles at \(40\) minutes, Keandra maintains this distance for \(20\) minutes, from \(40\) to \(60\) minutes. This flat, horizontal line signifies that she has paused or is stationary, and her distance from home does not change during this interval.
Once she resumes traveling at \(60\) minutes, her distance increases again, rising from \(50\) miles to \(100\) miles by \(80\) minutes. This demonstrates another phase of active traveling as she covers an additional \(50\) miles.
Finally, from \(80\) minutes to \(120\) minutes, the graph shows a significant decrease in distance, falling back to \(50\) miles. This leads to a second horizontal line that indicates Keandra is once again at a stationary point, remaining at \(50\) miles for \(40\) minutes.
In summary, Keandra's journey can be segmented into phases of increasing travel, periods of constant distance, and no average decrease during the observed time frame. The intervals collectively outline her movement pattern and suggest a structured journey that involves both travel and periods of rest.