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The problem you're working on involves determining a function that models the paint coverage in terms of the number of gallons of paint used. Let me break it down step by step:

### Part 1: Verbal definition of the function

A student discovers that 1 gallon of paint covers **200 square feet**. The question asks you to choose the correct verbal definition of the function. 

The correct answer is:
- **Option D: The number of square feet of coverage is 200 times the number of gallons of paint used.**

This is because each gallon covers 200 square feet, so if you use \( n \) gallons, the coverage will be \( 200n \) square feet.

### Part 2: Symbolic definition of the function

You are asked to write the symbolic definition of the function. The number of square feet of coverage \( s \) is related to the number of gallons of paint \( n \) by the equation:

\[
s = 200n
\]

This formula shows that the square footage \( s \) increases by 200 for each gallon \( n \) of paint used.

### Part 3: Numerical definition of the function (table completion)

The table shows how many square feet are covered as the number of gallons of paint \( n \) increases. Based on the function \( s = 200n \), we can fill out the table as follows:

| Number of gallons of paint, \( n \) | Square feet covered by the paint, \( s \) |
|------------------------------------|-----------------------------------------|
| 1                                  | 200                                     |
| 2                                  | 400                                     |
| 4                                  | 800                                     |
| 6                                  | 1200                                    |

This is simply multiplying the number of gallons by 200, which gives the amount of coverage in square feet.

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Do you need more details or have any other questions on this? Here are 5 additional questions to expand your understanding:

1. How would the function change if each gallon of paint covered a different number of square feet?
2. How could you express this function as an inverse function?
3. What would the graph of this function look like, and what are its key characteristics (e.g., slope, y-intercept)?
4. How would you calculate the number of gallons needed to cover a specific area, say 1000 square feet?
5. How would the function change if, for example, 2 gallons were wasted and didn't contribute to coverage?

**Tip:** Always verify your understanding of the relationship between variables by checking how one quantity depends on the other in real-life contexts.

A student is tasked with determining paint coverage based on the number of gallons of paint used, where 1 gallon of paint covers 200 square feet. The problem asks to define the function verbally, symbolically, and numerically.

This page explains how to calculate paint coverage using a linear function based on the number of gallons of paint. The function relates square feet covered and gallons used. Suitable for Grades 9-11.

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