COCO H.

asked • 03/27/15# CAN A FUNCTION HAVE AN INFINITE NUMBER OF VALUES IN ITS DOMAIN AND ONLY A FINITE NUMBER OV VALUES IN ITS RANGE

Can a function have an infinite number of values in its domain and only a finite number in its range?

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## 3 Answers By Expert Tutors

Hi Coco,

Yes, you could have a function like f(x) =2

the domain is all real numbers and the range is a single number

Hope this helps

Michael J. answered • 03/27/15

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Effective High School STEM Tutor & CUNY Math Peer Leader

Michael F.

There is a difference between bounded and finite. The range of the real sine function is the set of all reals from -1 to plus 1 inclusive, an infinite bounded set.

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03/28/15

Michael F. answered • 03/27/15

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Mathematics Tutor

Yes. As an example of such a function, let the domain be the interval

[0,1] on the x-axis and let the function have the value 0 at each of the rational points of that interval and 1 at each of the irrational points.

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