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## Topic A: Functions

# Recognizing functions from verbal description word problem

CCSS.Math: ,

## Video transcript

Jada 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 can
the amount of order be represented as a
function of shipping-- let me do that in
that blue color costs. So if we have the shipping
costs as an input, will 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, we have to input a shipping
cost, a shipping cost 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, 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 just has to be
anything less than $20. So it could have been $1. It could have been $1.50. It could've been $7. It literally can take
on any value up to $20. So it could even be $19.99. We could do a similar
thing if we input 7 into this relationship. If 7 was-- and I could put
literally an infinite number of numbers. It could be a million dollars. So if I input 7 into
this relationship that we're trying to test
whether it's a function, if 7 is the shipping costs,
then the order we just know is over $20, $20 or more. So it could be $20. It could be $800. It could be $1 million. There's actually an
infinite number of values that it could take
on right over here. So because for a
valid shipping cost, for each of these
valid shipping costs, I can get many, many,
many potential outputs, I don't know which output it
necessarily will output to. If someone tells you
the shipping costs and 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 cost. So, no.