The table shows the price of Speedgrow fertilizer. Because of a supply shortage, the manufacturer avoids selling more than 100 pounds to any single buyer. If the payment made by buyers is written as a function, f(x), of the amount of fertilizer, x, what will the range of payment from any single buyer be?

*50 lbs or less = $1.20
*51 lbs through 100=$1.10

Question

The table shows the price of Speedgrow fertilizer. Because of a supply shortage, the manufacturer avoids selling more than 100 pounds to any single buyer. If the payment made by buyers is written as a function, f(x), of the amount of fertilizer, x, what will the range of payment from any single buyer be?

*50 lbs or less = $1.20
*51 lbs through 100=$1.10

ciarán95 · Answer

Hi @liveinthewoods ! I'm not just entirely sure as to how you would go about writing a function to describe the payment being made by a buyer based on the amount of fertilizer they buy, but I don't think you need to do this in order to answer this question.

When we talk about the 'range of payment' from any single buyer, I presume it's referring to all of the possible amounts of money the buyer can hand over in order to purchase the fertilizer. In maths, the range is usually defined as:

(The largest value in a set of data) - (The smallest value in a set of data)

So, we know that no single buyer can buy more than 100 lbs (pounds). For everyone purchasing less than 50 lbs, they pay $1.20. For everyone purchasing between 51 and the maximum of 100 lbs, they pay $1.10. In this case, no matter how much fertilizer the buyer wants, they will end up handing over one of these two amounts of money. 

Therefore, we should be able to find the range in the possible payments made by buyers by subtracting these from one another (largest - smallest), thus giving us our answer.