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## Algebra 1

### Course: Algebra 1 > Unit 8

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(28 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(9 votes)
- Shouldn't the input be the shipping order? Why is it the shipping cost?(5 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 understand that we can have the same x but they y has to be the same number(2 votes)
- Can I also define this function as "If X is greater than twenty, add seven, if not add four"?(1 vote)
- Technically, you could, but it would be better defined in intervals. If x is less than or equal to 20, y=x+4 and if x is greater than 20, y=x+7. It is a function, but it has a discontinuity at 20 jumping from 24 with a closed circle to 27 with an open circle.(3 votes)

- hey what are a dependent and independent quantity(1 vote)
- A dependent quantity "depends" on an independent quantity. Most common independent variable (x) and dependent variable (y) in math, but many formulas in math and science have different variables. If you have y=3x+4, we call x independent because we can put in a value for x and find a value for the dependent variable y.(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) - Is there a way for this to be represented as an inequality? Example being, when x=4 Y is greater than 0, but less than 20?(2 votes)
- The definition of a function is that each input creates only one output. If the output can be greater than 0 but less than 20, then there are multiple ouputs for one input. This violates the defintion of a function.(1 vote)

- what is a ratio??(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.