Your Favorite Dog Groomer Pricing Model
a) What is the piecewise function that describes what your dog groomer charges?
Given: Your favorite dog groomer charges according to your dog's weight. If your dog is 15 pounds and under, the groomer charges $35. If your dog is between 15 and 40 pounds, she charges $40. If your dog is over 40 pounds, she charges $40, plus an additional $2 for each pound.
b) How would the graph of the function look like?
a) Piecewise Function
When your dog is 15 pounds and under, then the groomer charges $35.
f(x) = 35 when x ≤ 15
When your dog is between 15 and 40 pounds, then she charges $40.
f(x) = 40 when 15 < x ≤ 40
When your dog is over 40 pounds, then she charges $40, plus an additional $2 for each pound.
f(x) = 40 + 2(x - 40) when x > 40
b) Graph of the Function
Putting all the cases together, we get:
f(x) = { 35 when x ≤ 15, 40 when 15 < x ≤ 40, 40 + 2(x - 40) when x > 40 }
The graph of the function would show different linear segments based on the weight ranges mentioned above.
The piecewise function describing the pricing model of your favorite dog groomer captures the variation in charges based on your dog's weight. The function consists of different rules for different weight ranges to determine the grooming cost accurately.
For dogs weighing 15 pounds and under, the groomer charges a flat rate of $35. This is represented by the function f(x) = 35 when x ≤ 15, where x represents the weight of your dog.
If your dog falls between 15 and 40 pounds, the grooming fee increases to $40. The corresponding function is f(x) = 40 when 15 < x ≤ 40, indicating the price change for this weight range.
For dogs weighing over 40 pounds, the groomer charges a base fee of $40, along with an additional $2 for each pound above 40. This rule is modeled by the function f(x) = 40 + 2(x - 40) when x > 40, where the variable x denotes the weight of your dog.
By combining these rules into a piecewise function, the overall pricing model is accurately captured. The graph of the function would display distinct linear segments for each weight range, showcasing the pricing structure visually.