C = {(9, 1) (8, -3) (7, 5) (-5, 3)} is it a function?

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Alan P. Share
Sep 21, 2017

Answer:

As an alternative to the other answer (probably below this one)
Yes

Explanation:

It is not unusual to specify a finite/discrete function as a set of paired values where each pair represents a mapping of a Domain value to a Range value.

The limitation required for such a mapping to be a function is that any Domain value may only occur once within the defining set.

#{: ("Set pairs:",color(white)("xx")|color(white)("xx"),"Domain value",color(white)("xxx"),"Range value"), ((9,1),color(white)("xx")|color(white)("xx"),color(white)("xxx")9,color(white)("x")rarrcolor(white)("x"),color(white)("xxx")1), ((8,-3),color(white)("xx")|color(white)("xx"),color(white)("xxx")8,color(white)("x")rarrcolor(white)("x"),color(white)("xx")-3), ((7,5),color(white)("xx")|color(white)("xx"),color(white)("xxx")7,color(white)("x")rarrcolor(white)("x"),color(white)("xxx")5), ((-5,3),color(white)("xx")|color(white)("xx"),color(white)("xx")-5,color(white)("x")rarrcolor(white)("x"),color(white)("xxx")3) :}#

Note that the Domain values: #9, 8, 7, -5# are all unique and therefore no single domain value can map into multiple Range values. This is the basic definition of a function.

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Sep 21, 2017

Answer:

No.

Explanation:

This is just a set of coordinates. A function is a mapping that takes an element from a domain and maps it to one element in a range.
The set of coordinates may well come from a function, but they are not the function itself.

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