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Current time:0:00Total duration:3:23

Recognizing functions from verbal description word problem

CCSS.Math: ,

Video transcript

Jayda is ordering Mother's Day gifts online the shipping costs are based on the dollar amount of the order for orders less than $20 shipping costs $4 for orders $20 or more shipping is $7 can the dollar amount of the order be represented as a function of shipping costs so they're saying can the dollar amount of the order so it can the amount of order be represented as a function of shipping do that in that blue color can be represented as a function of shipping shipping costs so if we have shipping costs as an input well that map to exactly for a given input will we get exactly one output for the amount of order in order for this to be represented as a function in order for this to be represented as a function we have to input a a shipping cost a shipping cost where we where this relationship is defined we need to input a shipping cost put it into our relationship and get exactly one dollar amount of the order in order for this to be a function if we get multiple dollar amounts of the order then the relationship it's well it's still a relationship but it's not going to be a function so let's think about it what are the possible inputs here well there's only two possible shipping costs shipping costs are either going to be $4 or they're going to be $7 so let's think about what happens when we input $4 in as a shipping cost so if we input $4 into our relationship so we input $4 into our little potential function box so $4 into it what is the output what is going to be the amount of the order well if the shipping cost is $4 the amount of the order the amount of the order could it just has to be anything less than $20 so it could have been $1 it could have been in dollar-fifty it could have been $7 it literally can take on any value between up to 20 up to $20 so it could even be $19.99 we could do a similar thing if we inputted 7 into this relationship if 7 was that I could put literally an infinite number of numbers it could be a million dollars so if I input 7 into this put this relationship that we're trying to test whether it's a function if 7 is the shipping cost then the order we just know is over $20 $20 or more so it could be $20 it could be $800 it could be it could be $1,000,000 so it's actually an infinite number of values that it could take on right over here so because for a valid for a valid shipping cost I can for each of these valid shipping costs I can each I can get many many many potential outputs I don't know which output it necessarily will output to 4 if you if someone tells you the shipping cost you don't necessarily know what the order size was this is not a function you cannot represent the amount of order as a function of the shipping costs so know