Question
(dumb it down a lot and make it seem like an 8th grader wrote it with only three sentences per part/question)
The graph shows the depth of water, in feet, of a water tank over a certain amount of time, in minutes.
graph with the title water tank with the x axis labeled time in minutes and the y axis labeled depth in feet, with a line segment from 0 comma 0 to 40 comma 4, a line segment from 40 comma 4 to 60 comma 4, a line segment from 60 comma 4 to 100 comma 3, a line segment from 100 comma 3 to 140 comma 3, and another line segment from 140 comma 3 to 180 comma 0
Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant. (3 points)
Part B: What are the domain and range of the relation? (3 points)
Part C: Does the graph represent a function? Explain your reasoning. (3 points)
Part D: Write a real-world description of the graph. (3 points)
The graph shows the depth of water, in feet, of a water tank over a certain amount of time, in minutes.
graph with the title water tank with the x axis labeled time in minutes and the y axis labeled depth in feet, with a line segment from 0 comma 0 to 40 comma 4, a line segment from 40 comma 4 to 60 comma 4, a line segment from 60 comma 4 to 100 comma 3, a line segment from 100 comma 3 to 140 comma 3, and another line segment from 140 comma 3 to 180 comma 0
Part A: Identify the interval(s) where the graph is increasing, decreasing, and constant. (3 points)
Part B: What are the domain and range of the relation? (3 points)
Part C: Does the graph represent a function? Explain your reasoning. (3 points)
Part D: Write a real-world description of the graph. (3 points)
Answers
GPT-4o mini
**Part A:**
The graph is increasing from 0 to 40 minutes. It is constant from 40 to 60 minutes, and it is decreasing from 60 to 180 minutes. So we have an increase, a flat part, and then a decrease.
**Part B:**
The domain of the graph is from 0 to 180 minutes since those are the times shown. The range is from 0 feet to 4 feet for the water depth. So, the domain is [0, 180] and the range is [0, 4].
**Part C:**
Yes, the graph represents a function because each time (x-value) has only one depth (y-value). For example, at 60 minutes, the depth is always 4 feet. There are no times where the depth goes to two different levels.
**Part D:**
This graph shows how much water is in a tank over time. The water goes up to 4 feet, stays the same for a bit, and then goes down. Finally, the tank is empty after 180 minutes.
The graph is increasing from 0 to 40 minutes. It is constant from 40 to 60 minutes, and it is decreasing from 60 to 180 minutes. So we have an increase, a flat part, and then a decrease.
**Part B:**
The domain of the graph is from 0 to 180 minutes since those are the times shown. The range is from 0 feet to 4 feet for the water depth. So, the domain is [0, 180] and the range is [0, 4].
**Part C:**
Yes, the graph represents a function because each time (x-value) has only one depth (y-value). For example, at 60 minutes, the depth is always 4 feet. There are no times where the depth goes to two different levels.
**Part D:**
This graph shows how much water is in a tank over time. The water goes up to 4 feet, stays the same for a bit, and then goes down. Finally, the tank is empty after 180 minutes.