https://file.aiquickdraw.com/mathbot/file/17258469041622x1m34gm.jpg

The function provided in the image defines the pricing for a dog groomer based on the dog's weight, $ x $, in pounds. The piecewise function is defined as follows:

\[
f(x) = \begin{cases} 
35 & \text{if } 0 < x \leq 15 \\
40 & \text{if } 15 < x \leq 40 \\
40 + 2(x - 40) & \text{if } x > 40 
\end{cases}
\]

The problem asks: If your dog weighs 55 pounds, how much will you pay?

### Step-by-Step Solution:

1. Since the dog's weight, $ x = 55 $, is greater than 40, we will use the third part of the piecewise function:

\[
f(x) = 40 + 2(x - 40)
\]

2. Substitute $ x = 55 $:

\[
f(55) = 40 + 2(55 - 40)
\]

3. Simplify the expression:

\[
f(55) = 40 + 2(15) = 40 + 30 = 70
\]

### Answer: 
If your dog weighs 55 pounds, you will pay **$70**.

Would you like a detailed breakdown of any part of this solution or have other questions?

Here are some follow-up questions related to this function:

1. What would the cost be if your dog weighed 20 pounds?
2. How much would you pay if your dog weighed exactly 40 pounds?
3. For what weight range would the cost be exactly $40?
4. How does the function behave if the dog's weight is less than or equal to 15 pounds?
5. What is the rate of increase in cost per pound for dogs weighing more than 40 pounds?

**Tip:** Piecewise functions are useful in situations where different rules apply to different intervals of input values.

Your dog groomer charges according to the following function with f(x) representing the total price and x representing the weight of the dog in pounds. If your dog weighs 55 pounds, how much will you pay?

Learn how to calculate dog grooming costs using a piecewise function based on your dog's weight. This problem provides a step-by-step solution for a 55-pound dog, covering key math concepts like piecewise functions and linear relationships. Ideal for students in Grades 7-10.

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