At the supermarket checkout, the scanner records prices of foods you purchase. To protect consumers, state of Michigan passed the "scanning law" which says something similar to following:
If there is the discrepancy between price marked on item and price recorded by scanner, consumer is entitled to receive 10 times difference between the prices; this amount given should be at least $1 and at most $5. Also, consumer will be given difference between prices, in addition to amount computed above.
For example: If difference is 5¢, you must receive $1 (as 10 times difference is only 50¢ and you are to receive at least $1), plus difference of 5¢. Thus, total you must receive is $1.00 + $0.05 = $1.05, If difference is 25¢, you must receive 10 times difference additionally to difference, giving (10)(0.25) + 0.25 = $2.75. If difference is 95¢, you must receive $5 (because 10(.95) = $9.50 is more than $5, maximum penalty), plus 95¢, giving 5 + 0.95 = $5.95.

(a) Find lowest possible refund?

(b) Assume x is difference between price scanned and price marked on item, and y is amount refunded to customer. Write the formula for y in terms of x.

(c) Find difference between price scanned and price marked have to get the $9.00 refund?

(d) Graph y as the function of x.