https://file.aiquickdraw.com/mathbot/file/1726070991090ikvse0rd.jpg

https://file.aiquickdraw.com/mathbot/file/1726070991093zl4z9p6b.jpg

Let's break down the problem step by step based on the information visible in the screenshots.

### Part A:
1. **Y-intercept:** The graph shows the altitude starts at 9,000 meters. So, the y-intercept is 9,000 meters.
2. **X-intercept:** The graph touches the x-axis at 50 seconds, meaning the altitude becomes 0 at this point. So, the x-intercept is 50 seconds.
3. **Domain:** The time starts at 0 seconds and ends at 50 seconds, so the domain is \([0, 50]\) seconds.
4. **Range:** The altitude varies from 0 meters to approximately 9,500 meters. So, the range is \([0, 9,500]\) meters.

### Part B:
This part requires an interpretation of what the y-intercept, x-intercept, domain, and range mean in terms of the situation (altitude over time).

1. **Y-intercept:** It represents the initial altitude of the object, which is 9,000 meters.
2. **X-intercept:** It represents the time when the object reaches the ground (altitude 0), which is 50 seconds.
3. **Domain:** It represents the time period from the start to when the object hits the ground, so from 0 to 50 seconds.
4. **Range:** It represents the possible altitudes the object can reach, from 0 to 9,500 meters.

### Part C:
1. **Increasing interval:** The altitude seems to be increasing from 0 to approximately 10 seconds, reaching 9,000 meters.
2. **Decreasing interval:** The altitude decreases after 20 seconds, and the graph shows that it descends after reaching approximately 9,250 meters at 20 seconds.
3. **Average rate of change:** This can be calculated using the formula for the average rate of change, which is:
   \[
   \text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{0 - 9000}{50 - 0} = \frac{-9000}{50} = -180 \text{ meters/second}.
   \]
   So, the average rate of change for the entire flight is \(-180\) m/s.

### Questions to Expand:
1. What does the average rate of change tell you about the object's movement over time?
2. How would the graph change if the maximum altitude was higher?
3. What other interpretations can be made from the graph's shape?
4. How would the domain and range change if the time extended beyond 50 seconds?
5. Can we estimate the object's speed during the increase and decrease phases?

### Tip:
When analyzing a graph, always pay attention to both axes, as they provide critical information about the variables being compared.

The original question submitted by the user as text.

Explore the descent of an object as shown in a graph detailing altitude over time. This guide provides insights into calculating x-intercepts, y-intercepts, domain, range, and average rate of change. Suitable for high school students in Grades 10-12.

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