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## Algebra (all content)

### Course: Algebra (all content) > Unit 7

Lesson 7: Recognizing functions- Recognizing functions from graph
- Does a vertical line represent a function?
- Recognize functions from graphs
- Recognizing functions from table
- Recognize functions from tables
- Recognizing functions from verbal description
- Recognizing functions from verbal description word problem

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# Recognizing functions from verbal description word problem

CCSS.Math: ,

Checking whether a description of the price of an order can be represented as a function of the shipping cost. Created by Sal Khan.

## Want to join the conversation?

- Can the
**shipping cost**be represented as**a function of**the**dollar amount of the order**?(25 votes)- Yes, because when you input the dollar amount of the order you will get one price for shipping. So we would see that when x<20 then f(x) =4 and when x≥20 then f(x) = 7(30 votes)

- Amount(shipping cost) is NOT a function. shipping cost (amount) IS a function because for any given amount there is only one possible output(11 votes)
- Is it just me or does this make no sense :D(10 votes)
- Shouldn't the input be the shipping order? Why is it the shipping cost?(6 votes)
- because the question is asking "Can the dollar amount of the order be represented as a function of shipping cost?" The word
**represented**means the opposite! so that's why shipping cost is the input! good question Varin Nair!(4 votes)

- I seriously do not understand this(2 votes)
- Well if

Shipping cost(y) is output and

amount of order(x) is input, then

y=4 when x<20, and

y=7 when x>20.

This means that the shipping cost is the function for the amount of dollar right?

Cos various inputs can have one output but one input can't have various outputs in functions. Right?(2 votes) - what is a ratio??(1 vote)
- Why is the shipping cost higher if you pay more. It seems like it should be the other way around, right?(1 vote)
- Why do you think that it would be less expensive to ship more stuff? The package would be bigger and heavier which would cost more to ship depending on what is being shipped.

On the other hand, many companies will give you free shipping once you have reached x amount of dollars (often over 100 dollars) which encourages you to buy more stuff. Also, scales do go down on many scales (4 dollars less than 20, 7 dollars between 20 and 40 which is a dollar cheaper than 2 20 dollar buys, then maybe 9 dollars for 40 to 60 dollars, and free shipping over 60 dollars.

Seldom do companies charge 4 dollars for less than 20 then only 3 dollars for over 20 dollars.(2 votes)

- Are there ways to describe this relationship besides a function? I don't think you could describe it with an equation, so what is this?(1 vote)
- But if you say that the shipping cost is a function of the amount order then it is a functional relationship(1 vote)

## 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.