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Recognizing functions from verbal description word problem
Checking whether a description of the price of an order can be represented as a function of the shipping cost. Created by Sal Khan.
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- 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(8 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)
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.