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)

Question

Responses

amount; 1
amount; 1

weight; 10
weight; 10

weight; 1
weight; 1

amount; 10
amount; 10

Answer 1

To create a piecewise linear graph of the dog boarding fee structure based on weight, we need to define the x-axis in terms of weight (the independent variable) and the corresponding fee amount (the dependent variable).

The best choice for the x-axis is "weight," as we are graphing the charges based on the dog's weight.

Now let's examine the increments for weight to cover all relevant sections of the piecewise function:

1. For dogs under 15 lbs, it charges $30.
2. For dogs between 15 and 50 lbs, the charge is $35.
3. For dogs 50 lbs or more, the charge starts at $35 and increases $3 for every additional 5 lbs over 50 lbs.

To accommodate these changes while ensuring clarity in the graph, a weight increment of 10 lbs would allow for clear representation of charge increases in each section without overly detailing smaller increments.

Thus, the best definition for the x-axis quantity and scale for a piecewise linear graph of the fee structure is:

weight; 10