The image shows a graph where the speed (in miles per hour) is plotted against time (in minutes). The graph starts at a speed of 5 miles per hour and decreases at certain intervals. Below the graph, a multiple-choice question is asking for the correct description of the graph, specifically which range of values best describes the behavior of $y$, where $y$ represents speed.

Analysis of the Graph:

1. From 0 to 30 minutes, the speed remains constant at 5 miles per hour.
2. From 30 to 40 minutes, the speed drops from 5 to 3 miles per hour.
3. From 40 to 90 minutes, the speed remains constant at 3 miles per hour.

Answering the Multiple Choice:

• Option A (3 ≤ y ≤ 5): This is correct because the speed is between 3 and 5 miles per hour throughout the graph (it stays at 5, then drops to 3).
• Option B (y = 5): This is incorrect because the speed is not always 5; it drops to 3 after 30 minutes.
• Option C (y ≥ 0): This is incorrect because although speed is non-negative, the correct range is between 3 and 5.
• Option D (0 ≤ y ≤ 5): This is incorrect because the minimum speed in the graph is 3, not 0.

Correct Answer:

Option A: 3 ≤ y ≤ 5

Would you like more details on this, or do you have any questions?

Here are five related questions you might find interesting:

1. What is the significance of the slope in a graph like this?
2. How can the relationship between speed and time be described using a piecewise function?
3. How would you calculate the total distance traveled based on this graph?
4. What does a horizontal line in a speed-time graph represent?
5. How does this graph change if the speed increases instead of decreasing after 30 minutes?

Tip: In speed-time graphs, the area under the curve represents the distance traveled!