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# Recognizing functions from verbal description word problems

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?
• 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
• Amount(shipping cost) is NOT a function. shipping cost (amount) IS a function because for any given amount there is only one possible output
• Is it just me or does this make no sense :D
• Shouldn't the input be the shipping order? Why is it the shipping cost?
• 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!
• Am i right in saying that the shipping cost can be represented as a function of the amount of the order?
• I think it can be a function!

f(order) = shipping cost

if order < \$20 --> shipping cost \$4
if order >= \$20 --> shipping cost \$7

As you can see, no matter what number you give as an input you only have one possible output. An order can't have a shipping cost of \$7 AND \$4 at the same time.
• hello I need help learning math
• There are a lot of KA users that reply to posted questions. So, to get help, post a specific question about the video about what you don't understand. You will most likely get a response.
• it wont let me go on to my next lesson even tho i already did this one twice :(
• Sounds like you need technical support -- Use the "Help Center" link that is at the bottom of all KA screens.
• Hi everyone, Can anyone tell me why shipping cost is an input...
• Wait but I thought, x can't repeat but only y can. Isn't that what's happenign?
(1 vote)
• But 𝑥 is repeating.
𝑦 = 1 ⇒ 𝑥 = 4.
𝑦 = 2 ⇒ 𝑥 = 4.
We have the same 𝑥-value for different 𝑦-values.
Thereby 𝑦 is not a function of 𝑥.
• 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?

## 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.