Question

Your favorite dog groomer charges according to your dog's weight. If your dog is 15 pounds and under, the groomer charges a flat fee of $35. If your dog is between 15 pounds and up to 40 pounds, then she charges a flat fee of $40. If your dog is over 40 pounds, then she charges $40 plus an additional $2 for every pound the dog is over 40 pounds.

Let (w) represent the weight of the dog. Which of the following piecewise functions represents the above problem?

a) (f(w) = begin{cases} 35 & {if } w ≤15 40 & {if } 15 < w ≤40 40 + 2(w - 40) & {if } w > 40 end{cases})
b) (f(w) = begin{cases} 35 & {if } w ≤15 40 & {if } 15 < w ≤40 40 + 2w & {if } w > 40 end{cases})
c) (f(w) = begin{cases} 40 & {if } w ≤15 35 & {if } 15 < w ≤40 40 + 2(w - 40) & {if } w > 40 end{cases})
d) (f(w) = begin{cases} 40 & {if } w ≤15 40 + 2(w - 15) & {if } 15 < w ≤40 40 + 2(w - 40) & {if } w > 40 end{cases})

Answer 1

The correct piecewise function representing the dog grooming charges based on weight is option (a), which correctly outlines the different pricing tiers for various weight ranges.

Step-by-step explanation:

The correct piecewise function that represents the groomer's charging scheme depending on the dog's weight (w) is:

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

This function describes the cost to groom a dog based on three weight categories. For dogs weighing 15 pounds or less, the charge is a flat fee of $35. For dogs weighing more than 15 pounds but up to 40 pounds, the charge is a flat fee of $40. Lastly, for dogs weighing over 40 pounds, the charge is $40 plus an additional $2 for every pound over 40.