The graph in the image shows velocity (in m/min) as a function of time (in minutes). I'll analyze the graph and answer the five questions step by step:

1. What interval shows a constant velocity over time?

A constant velocity occurs when the graph is horizontal (no slope). From the graph:

• A constant velocity is shown between 10 minutes and 15 minutes, where the velocity remains at 60 m/min.

Answer: [10, 15]

2. What interval shows the graph decreasing?

The graph decreases when the slope is negative (velocity is decreasing):

• The interval where the graph decreases is 15 minutes to 30 minutes, as the velocity drops from 60 m/min to -40 m/min.

Answer: [15, 30]

3. After 20 minutes, what would the velocity be according to the graph?

• At 20 minutes, the graph's velocity is approximately 40 m/min. This is based on the linear decrease from 60 m/min (at 15 minutes) to -40 m/min (at 30 minutes).

Answer: 40 m/min

4. What is the domain for this function?

• The domain represents the range of time values on the graph.
• Time starts at 0 minutes and ends at 50 minutes.

Answer: [0, 50]

5. Is this linear or nonlinear?

• The graph is composed of straight-line segments, indicating a linear relationship within each interval.

Answer: Linear

Let me know if you'd like further explanations for any question!

Here are five related questions to deepen your understanding:

1. How can you calculate the slope of each segment on the graph?
2. What does the slope represent in this velocity-time graph?
3. How would the graph change if acceleration were involved?
4. What does the negative velocity indicate in this graph?
5. How do you calculate displacement from this velocity-time graph?

Tip: The area under a velocity-time graph gives the displacement over the interval!