For a piecewise linear graph representing the fee structure of the dog boarding facility based on weight, the x-axis will represent the dog's weight, and the scale should effectively cover the different weight categories defined in the fee structure.
The categories are:
- Dogs under 15 lbs: $30
- Dogs between 15 lbs and 50 lbs: $35
- Dogs 50 lbs or more: $35 plus $3 for each additional 5 lbs over 50 lbs
Given these groups, the weight range would span from just below 15 lbs to the maximum possible weight of a dog. Therefore, an appropriate scale for the x-axis would cover the range of weights effectively, allowing for clarity in displaying the charges for different weights.
The term "weight" as the quantity on the x-axis is appropriate, and given the usual unit of measurement for dog weight in pounds, a scale increment of 10 lbs would effectively represent the various weight categories and keep the graph readable.
Thus, the best definition for the quantity and scale for the x-axis would be:
weight; 10