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    Z x Z functions and range

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    See the attached file.
    Consider the set of integers Z. The set Z x Z consists of all ordered pairs of integers. In symbols,
    Z x Z={(x,y):x,y∈Z}

    For example, (2,-5) , (0,0) , (-127,10) , and (-5,2) are all distinct elements of Z x Z.
    Notice that the order matters; (2,-5) and (-5,2) are different elements of Z x Z.
    Now let?s define a few functions on Z x Z:

    f(x,y)=x*y
    (See the attached file for full equations)
    h(x,y)=x^y

    (a) What is the range of each of these functions? In other words, is the image an integer, a rational number or only a real number?

    (b) For which of these functions (if any) is the image of (x,y) equal to the image of (y,x)?

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    https://brainmass.com/math/computing-values-of-functions/zxz-functions-range-465834

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    See the attached file.
    6. Consider the set of integers. The set x consists of all ordered pairs of integers. In symbols,
    x

    For example, (2,-5) , (0,0) , (-127,10) , and (-5,2) are all distinct elements of x .
    Notice that the order matters; (2,-5) and (-5,2) are different elements of x .
    Now let's define a few functions on x :

    (a) What is the range of ...

    Solution Summary

    The solution examines Z x Z functions and range.

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