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Functions with real numbers and integers

All of the functions below follow the equation f(x) = x^2. However, they have different domains and co-domains. Match each to its properties. Remember, Z = the set of integers, R = the set of real numbers, R+ is the set of positive real numbers, R(nonneg) is the set of nonnegative real numbers.


* f: Z -> Z
* f: R+ -> R
* f: R -> R(nonneg)
* f: R+ -> R+


* not one-to-one: not onto
* not one-to-one; onto
* one-to-one; onto
* one-to-one: not onto

Solution Summary

This takes a look at four functions that map real numbers, positive reals, or integers onto reals, positive reals, or integers. It then matches them with the appropriate classification of one-to-one or onto.