Please HElP: If an iteam cost more than $175 it has a sale tax. In that case, the state charges 5% tax on the amount over $175. How can I write a piecewise function that gives me the total cost including the tax of an item of clothing priced at P dollars ?

Question

calculusxy · Answer

(175*0.05)=P and then add the P answer to 175? (I think that's how but just check)

anonymous · Answer

Will that give me a piecewise function for any item that is sold ?

anonymous · Answer

I'll give this a try... me an equation writer have not been having a good day:
$$f(P) = \left\{  0<= P <= 175 then f(P)=175 \right\ ; P > 175 then f(P) = P + .05(P-175) }$$

anonymous · Answer

Another try:
f(P) = {
0<=P <= 175 ; f(P) = P
P> 175; f(P) = P + .05(P-175)
}

Your particular notation will depend on your instructor.
Helpful a little?

Note that it is piecewise continuous because P is defined across all points. There is no gap.

anonymous · Answer

Please let me know if I helped. Regards, kj

anonymous · Answer

Thank you !