Question

Each person in this room is mapped to their birthday? is this a relation or a function? and why

Answer 1

probably not a function because two people would likely share a birthday

Answer 2

A function relates a set of inputs to a set of outputs. However, there is one important restriction for it to be a function. Each input can only have one output.

Answer 3

So if the input where people, the output would be their birthdays, is that a valid function?

Answer 4

yh but if the input has more than one its not a function, so its a relaction?

Answer 5

But the input is the people. They are all unique, right? If two unique people had the same birthday, would that be a problem? No, because each person(input) relates to exactly one birthday (output)

Answer 6

ohh soo it is a relation because from every input goes to an output so it is a function right??

Answer 7

every unique input is mapped to exactly one unique output, so it's a function indeed

Answer 8

yh thanks man :D can u explain me 1 more please

Answer 9

nice. a very subjective question wel handled.

Answer 10

x (the input) is mapped to 2x?
what is it

Answer 11

However, the other way around would NOT work. because the same birthdays could refer to multiple people

Answer 12

which means that f(x) = 2x

Answer 13

So how many times is 2x more than x?

Answer 14

2?

Answer 15

Indeed. So what's an other way of saying that something is 2 times more than something else?

Answer 16

f(x)2 something like that ? or x+x

Answer 17

Wel 2x = x+x but that was not my point.
My point is, that 2x, is the "double" of x

Answer 18

so the function maps x to it's double

Answer 19

And that's really all you can say about it. Because x is a variable, and it depends on the value you want to "plug" into it.

Answer 20

It's actually the other way around.

Answer 21

But I think I understand your question now. IS it a function or a relation? Well, does each unique input correspond to exactly one output?

Answer 22

ohh so x to 2x? is its a function ?

Answer 23

right

Answer 24

wait so there is two inputs from the same place ? so its nt relation its a function

Answer 25

Your input is x, your output is 2*(x), which is equal to (2*input)

Answer 26

All you need to determine is something is a function is that each unique input has to be mapped to one and only one output

Answer 27

aha now i see so the answer is its not a function?

Answer 28

So obviously, that's not a problem here. But let me ask you something now.

\[f(x) = \pm \sqrt{x^2}\]

Is this a function?

Answer 29

yes i guess

Answer 30

And about your question, it is a function. Each input has exactly one output.

Answer 31

But my question, is not a function

Answer 32

because x is mapped to both +sqrt(x^2) and -sqrt(x^2)

Answer 33

in order for it to be a function, it can only have one output for each input. This thing has two outputs for each input, so it's definitely not a function.

Answer 34

oh yeah yeah i mixed up i did the opposite

Answer 35

Do you understand now? :)

Answer 36

yeah inputs has only 1 output

Answer 37

yes thanxxx man :D i appreciate :)

Answer 38

no problem :)

Answer 39

In the case of the birthdays, it would not be a function if each person had two birthdays. This should make it clear!