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The problem asks to create a function $ g(x) $ to represent the total cost of renting the Jump Monster for $ x $ hours, which includes a $25 per hour rental fee and a one-time cleaning fee of $42. 

### Step 1: Initial Function
The given function is $ f(x) = 25x $, which represents the cost of renting the bounce house for $ x $ hours without the cleaning fee.

### Step 2: Adding the Cleaning Fee
The company adds a one-time fee of $42 for cleaning. So, to modify the function, we need to add 42 to the rental cost:

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

### Step 3: Filling in the Blanks
Looking at the format $ y = \_ x + \_ $, we fill in the coefficients:

\[
y = 25x + 42
\]

Thus, the correct values are:
- $ 25 $ for the coefficient of $ x $ (rental cost per hour).
- $ 42 $ for the constant (cleaning fee).

Would you like a further explanation? Here are five related questions you could explore:

1. How would the function change if the cleaning fee increased to $50?
2. What would the total cost be for renting the bounce house for 5 hours?
3. How would the function change if the company added a recurring hourly cleaning fee instead?
4. How does the slope of the function $ g(x) $ represent the rental cost per hour?
5. Can you calculate the cost of renting the house for zero hours (only the cleaning fee)?

**Tip:** Functions like these are linear, where the slope (coefficient of $ x $) represents a recurring cost, and the y-intercept (constant) is a fixed, one-time charge.

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 create a linear function that represents the total cost of renting a bounce house, factoring in hourly rates and a one-time cleaning fee. Ideal for students in Grades 6-8, this problem uses algebraic concepts.

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