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Let's break down the problem and solve it step by step.

### Given:
- \( P = 40N + 2400 \), where \( P \) is Miguel's total pay (in dollars) and \( N \) is the number of copies of **History is Fun** Miguel has sold.
- Miguel has 140 copies available to sell.

### 1. **Domain**:
The domain refers to the values that \( N \), the number of copies Miguel has sold, can take. Since Miguel can sell between 0 and 140 copies, the domain will be:
- **The number of copies Miguel has sold**.
- The set of values will be **\[0, 1, 2, ..., 140\]**.

### 2. **Range**:
The range refers to the values that \( P \), Miguel's total pay, can take. Since the equation for pay is \( P = 40N + 2400 \), let's evaluate \( P \) at the extremes of the domain (i.e., when \( N = 0 \) and \( N = 140 \)):

- When \( N = 0 \), \( P = 40(0) + 2400 = 2400 \).
- When \( N = 140 \), \( P = 40(140) + 2400 = 5600 + 2400 = 8000 \).

So, the range of \( P \) is from **2400 to 8000**. Therefore:
- **Miguel's total pay (in dollars)**.
- The set of values will be **\[2400, 2401, 2402, ..., 8000\]**.

### Final Answer:
- **Domain**: The number of copies Miguel has sold. Set of values: \[0, 1, 2, ..., 140\].
- **Range**: Miguel's total pay (in dollars). Set of values: \[2400, 2401, 2402, ..., 8000\].

Would you like further explanation or details on how these answers were derived?

Here are 5 related questions you might consider:
1. How would the function change if Miguel earned more per copy?
2. What is the significance of the constant 2400 in the equation?
3. Can we consider any negative values for the domain? Why or why not?
4. How does the slope of 40 in the equation affect Miguel's pay?
5. What would the domain and range be if Miguel had 200 copies to sell?

**Tip**: Always check the meaning of the variables in the context of the problem when determining domain and range.

Miguel is a software salesman. Let P be Miguel's total pay (in dollars). Let N be the number of copies of History is Fun he has sold. Suppose that P = 40N + 2400 gives P as a function of N for these available copies. Identify the correct description of the values in both the domain and range of the function.

Learn how to determine the domain and range of a linear function representing Miguel's total pay based on the number of copies of History is Fun sold. This problem involves calculating values for the function P = 40N + 2400, with key algebraic insights suitable for Grades 9-11.

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