5. Let X = {a, b, c) and Y = {d, e, f, g}.
Does the following arrow diagram determine a function from X to Y? Explain. (6 Pts)
b. What are the domain, and co-domain

- blackstreet23

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- blackstreet23

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## More answers

- DanJS

Look at what a function does, |dw:1443380326622:dw|

- blackstreet23

- blackstreet23

- blackstreet23

I am confused because it meets the two requirements

- blackstreet23

1. All x values have a y value

- blackstreet23

2. No same x value has two ys

- blackstreet23

but do they need to have the same number of elements in X and Y?

- blackstreet23

- blackstreet23

?

- blackstreet23

two x values can have the same why but not vice versa i think

- welshfella

yes
another way to say it is a function can be many-to-one but not one-to-many

- blackstreet23

yes @welshfella but is that one a function?

- blackstreet23

Do the elements on X and Y need to be the same number?

- welshfella

what is different with this relation is that you have values of y not linked with a value of x.
To be honest i don't know for sure.

- DanJS

the co-domain, is all of the output values, the set contains all of the 'graphed' points that are mapped by the rule X-->Y, Plus possibly more.

- DanJS

Like say for example, if you have the function
f(x) = x^2
The Domain is all real numbers, the range of that is just numbers greater than zero...

- welshfella

http://www.mathsisfun.com/sets/domain-range-codomain.html

- DanJS

the co-domain though is all real numbers,

- DanJS

x ---->x^2, both can be any real number, but the actual image of the graph does not have negative values, so the co domain includes the negative values, the range is just positive values

- blackstreet23

so the whole set Y is the codomain

- blackstreet23

it does not matter that some elements are not used?

- blackstreet23

- DanJS

right, the co-domain possibly includes values that aren't graphed by the function

- zepdrix

I found this kind of helpful :)
http://www.mathsisfun.com/sets/domain-range-codomain.html
If you scroll half-way down, the three green check marks.

- DanJS

f(x) = x^2
Domain - All Reals
Range - y >=0
co-domain - all reals

- DanJS

X ----> X^2
you can choose any number for X, domain
You can choose any number for X^2, co-domain
the results area always positive, Range or the actual graph

- blackstreet23

Yeah thanks ! I get it now

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