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Look at what a function does, |dw:1443380326622:dw|
I am confused because it meets the two requirements
1. All x values have a y value
2. No same x value has two ys
but do they need to have the same number of elements in X and Y?
two x values can have the same why but not vice versa i think
yes another way to say it is a function can be many-to-one but not one-to-many
Do the elements on X and Y need to be the same number?
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.
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.
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...
the co-domain though is all real numbers,
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
so the whole set Y is the codomain
it does not matter that some elements are not used?
right, the co-domain possibly includes values that aren't graphed by the function
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.
f(x) = x^2 Domain - All Reals Range - y >=0 co-domain - all reals
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
Yeah thanks ! I get it now