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Can a function have an infinite number of values and domain and only a finite number of values in its range?
Dejohntae
Sure. Remember that a function is ANY rule defined to calculate one number based on another number. You can define such a rule any way you want. For example, you can have a function which for ANY value in its domain, the result will always be 1 (or any other number you choose). Such a function (the constant function) will fulfill the requirements of the question. A more interesting (and more useful) example is the "sign" ("signum") function, defined with the following rule:
* For x < 0, f(x) = -1
* For x > 1, f(x) = 1
* For x = 0, f(x) = 0
This function has only three values in its range.
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