https://file.aiquickdraw.com/mathbot/file/1726095944277blfxjids.jpg

Let's analyze the graph and solve the problem based on its structure and details.

### Part (a) — On what days is the graph not continuous?

The graph shows the amount of gasoline in the tank over time (in days). In the graph, there are noticeable jumps where the amount of gas suddenly increases. This usually occurs when the person refuels the car. These points represent discontinuities because the gasoline level jumps up without a smooth transition.

From the graph, the discontinuities occur on:
- Day 6: There is a jump in the graph from around 2 gallons to 18 gallons.
- Day 18: There is another jump from around 4 gallons to 16 gallons.

Thus, the graph is not continuous on **days 6 and 18**.

### Part (b) — What do you think happens on these days?

Based on the context, the discontinuities correspond to the days when the person **fills up the gas tank**. The graph shows a sudden increase in gasoline, which can only happen when more fuel is added to the tank. So, on days 6 and 18, the person must be refueling their car.

Answer: **On these days, the person fills his or her gas tank.**

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Do you want more details or have any questions about this solution?

Here are five related questions to explore:

1. What does the slope of the graph represent in this context?
2. How would the graph change if the person drove at a constant speed without stopping?
3. What would a horizontal line on the graph indicate?
4. How would the graph look if the person used more gas over time?
5. What other events could cause a discontinuity in such a graph?

**Tip:** A graph's slope can give you insights into how fast a quantity is changing over time—whether it's fuel consumption or something else.

The graph shows the number of gallons G of gasoline in a person's car after t days. On what days is the graph not continuous? What do you think happens on these days?

Learn how to analyze a graph representing gasoline usage over time, focusing on identifying discontinuities and understanding real-world events that affect the graph's structure. Suitable for students in Grades 9-12.

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