A department store is offering a coupon for 21 off for any purchases over $100.
Construct a piecewise function for the actual cost, C, of the purchase as a function of the original purchase price, P.
C= ? ,if 0 <P </100
C = P if 0 < P <= 100
Now you can do the part where P > 100, right?
Thank you @steve
Whats p>100?
To construct a piecewise function for the actual cost, C, of the purchase as a function of the original purchase price, P, we need to consider two cases:
Case 1: When the original purchase price, P, is between 0 and $100 (exclusive)
For this case, since the coupon is only valid for purchases over $100, the actual cost, C, will be the same as the original purchase price, P, because no discount is applied.
Therefore, the piecewise function for this case is:
C = P
Case 2: When the original purchase price, P, is greater than or equal to $100
For this case, the coupon is applicable, and the discount of $21 will be deducted from the original purchase price, P, to calculate the actual cost, C.
Therefore, the piecewise function for this case is:
C = P - $21
To summarize, the piecewise function for the actual cost, C, of the purchase as a function of the original purchase price, P, is:
C = P, if 0 < P < 100
C = P - $21, if P ≥ 100