Question

A dog boarding facility charges daily based on a dog’s weight. If the dog weighs under 15 lbs, the rate is $30. If the dog is between 15 and 50 lbs, it is $35. If the dog is 50lbs or more, the charge is $35 plus $3 for each additional 5 lbs over 50 lbs. Which of the following best defines the quantity and scale for the x-axis for a piecewise linear graph of the fee structure?(1 point) Responses weight; 10 weight; 10 weight; 1 weight; 1 amount; 1 amount; 1 amount; 10

Answer 1

To define the quantity and scale for the x-axis of a piecewise linear graph of the fee structure based on the dog's weight, we need to consider the weight ranges provided:

1. Dogs under 15 lbs are charged a flat rate of $30.
2. Dogs between 15 lbs and 50 lbs are charged a flat rate of $35.
3. Dogs over 50 lbs incur additional costs based on how much they weigh over 50 lbs.

Given that the weight categories are defined in increments of 5 lbs, and that we need a range that comfortably includes all the weight categories (from 0 lbs up), the best choice for the scale on the x-axis would be increments of weight suitable to represent the various fee structure changes.

Considering the standard increments:

- The ranges are clearly defined at break points of 15 lbs and 50 lbs.
- Additionally, the increments of additional charges over 50 lbs occur every additional 5 lbs.

Thus, the best scale to represent the data would be in increments of 1 lb, allowing for precise tracking of weight changes up to at least the point where significant charge changes occur.

Therefore, the option that best defines the quantity and scale for the x-axis is:

**weight; 1**