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.
(a) Write a piecewise function that describes what your dog groomer charges.
(b) Graph the function.
(c) What would the groomer charge if your cute dog weighs 60 pounds?
Solution:
(a) We see that the “boundary points” are 15 and 40, since these are the weights where prices change. Since we have two boundary points, we’ll have three equations in our piecewise function. We have to start at 0, since dogs have to weigh over 0 pounds:
We are looking for the “answers” (how much the grooming costs) to the “questions” (how much the dog weighs) for the three ranges of prices. The first two are just flat fees ($35 and $40, respectively). The last equation is a little trickier; the groomer charges $40 plus $2 for each pound over 40. Let’s try real numbers: if your dog weighs 60 pounds, she will charge $40 plus $2 times 20 (60 – 40). We’ll turn this into an equation: 40 + 2(x – 40), which simplifies to 2x – 40 (see how 2 is the slope?). So the whole piecewise function is:
(a) Write a piecewise function that describes what your dog groomer charges.
(b) Graph the function.
(c) What would the groomer charge if your cute dog weighs 60 pounds?
Solution:
(a) We see that the “boundary points” are 15 and 40, since these are the weights where prices change. Since we have two boundary points, we’ll have three equations in our piecewise function. We have to start at 0, since dogs have to weigh over 0 pounds:
We are looking for the “answers” (how much the grooming costs) to the “questions” (how much the dog weighs) for the three ranges of prices. The first two are just flat fees ($35 and $40, respectively). The last equation is a little trickier; the groomer charges $40 plus $2 for each pound over 40. Let’s try real numbers: if your dog weighs 60 pounds, she will charge $40 plus $2 times 20 (60 – 40). We’ll turn this into an equation: 40 + 2(x – 40), which simplifies to 2x – 40 (see how 2 is the slope?). So the whole piecewise function is: