Create a situation that would require both the functions, f(x) and g(x), and is related to the situations you have already outlined. Use addition or subtraction to combine the functions.

Imagine a scenario where a company manufactures two types of products: **Product A** and **Product B**. The profit generated from selling a certain number of units of Product A can be modeled by the function \( f(x) \), and the profit from selling a certain number of units of Product B can be modeled by the function \( g(x) \), where \( x \) represents the number of units sold.

Now, suppose the company wants to calculate the **total profit** generated from selling both products. This situation would require the combination of the functions \( f(x) \) and \( g(x) \) using addition. The total profit \( P(x) \) from selling \( x \) units of both products can be represented by the equation:

\[
P(x) = f(x) + g(x)
\]

Alternatively, if the company needs to determine the **difference in profit** between the two products, they would use subtraction. The difference in profit \( D(x) \) can be represented by:

\[
D(x) = f(x) - g(x)
\]

This scenario illustrates how combining functions using addition or subtraction can help in understanding the overall or comparative profit from different products.

Would you like further details on this or have any questions? 

Here are 5 related questions to explore:

1. How would the situation change if one of the products had a varying cost per unit sold?
2. Can you create a scenario where one product has a linear profit function and the other has a quadratic profit function?
3. How could you use multiplication to combine the functions \( f(x) \) and \( g(x) \)?
4. What if the company offered a discount on both products, how would that affect the total profit function?
5. How would you interpret the derivative of the combined function \( P(x) \) in this context?

**Tip:** When combining functions, it's important to understand the context behind each function to ensure that the combination (addition, subtraction, etc.) makes logical sense and reflects the real-world situation accurately.

Explore how to combine functions using addition and subtraction to calculate total and difference in profits from two products. This example illustrates key algebraic concepts and function operations, making it suitable for students in Grades 9-11.

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