# A coupon gives $50 off your camera's purchase of $100 or more at zeke's camera world. Give a function relating a camera's purchase price after coupon y to the retail price x give the domain of...

A coupon gives $50 off your camera's purchase of $100 or more at zeke's camera world. Give a function relating a camera's purchase price after coupon y to the retail price x give the domain of this function. An online retailer currently offers a 40% discount on cameras, give a function relating a camera's purchase price after discount to the retail price x give the domain of this function. What is the minimum your camera purchase will cost for both the cases?

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### 1 Answer

The coupons allows the buyer to pay $50 less than the total amount on the bill when a camera worth $100 or more is bought.

If the price of the of the camera is x and the amount that the customer has to pay is P(x),

P(x) = x - 50, `x>= 100`

The domain of this function is `[100, oo)` .

The on-line retailer offers a discount of 40%. In this case if P(x) is what the customer pays and x is the price of the camera, P(x) = (1 - 0.4)*x = 0.6*x. The domain of the function is `(0, oo)`

The coupon can only be used for a camera that costs $100 or more. To determine the least amount that has to be paid, assume the cost of the camera is $100. At the on-line store the customer pays $60 and if the coupon is used the amount to be paid is $50.