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The problem states that the bounce house rental costs $25 per hour, represented by the function $ f(x) = 25x $, where $ x $ is the number of hours. Additionally, the company adds a one-time cleaning fee of $42.

We need to create a new function $ g(x) $ that includes both the hourly rate and the cleaning fee. This function will have the form:

\[
g(x) = 25x + 42
\]

This represents the total cost, where $ 25x $ is the hourly charge and $ 42 $ is the fixed cleaning fee.

So, the correct answer for $ Y $ would be:

\[
Y = 25x + 42
\]

Would you like further clarification on how this function is derived?

### 5 Related Questions:
1. How do you interpret linear functions like $ g(x) = 25x + 42 $ in terms of their slope and intercept?
2. What would the total cost be if the rental is for 3 hours?
3. How would the function change if the hourly rate increased to $30?
4. How can we graph this function to visualize the relationship between hours rented and total cost?
5. What is the significance of the cleaning fee in relation to the function's y-intercept?

### Tip:
Always remember that the constant term in a function like $ g(x) = 25x + 42 $ represents a one-time fixed cost, while the term multiplied by $ x $ represents a variable cost depending on usage or time.

A bounce house company rents the Jump Monster for $25 an hour. The function f(x) = 25x represents the rental fee for x hours. The company decides to add a one-time fee of $42 for cleaning. Write a function to represent g(x).

Learn how to represent the total cost of renting a bounce house, including both the hourly fee and a one-time cleaning fee. The problem uses a linear function g(x) = 25x + 42 to model the total cost. Suitable for students in Grades 6-8.

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