Help with domain and range

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
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Help with domain and range

Postby standardtoaster » Fri Dec 18, 2009 1:56 am

Domain and range is a bit confusing for me. I'm currently taking pre-calc. This is my first week of it and I have gotten most of it up until the test. I can't seem to get past the first question. :( Could you please help me out a bit?

Imagine a mapping from the set of all integers onto the set of all nonnegative integers in which the set of ordered pairs is:
{(0,0, (1,1), (-1,2), (2,3), (-2,4), (3,5), (-3, 6), (4,7), (-4,8),...}

Is this relation a function? If so, why? If not, why not? Is its inverse a function? If so, why? If not, why not?

I don't quite understand how I would approach this. Thank you for your help.
Last edited by standardtoaster on Mon Dec 21, 2009 7:55 pm, edited 1 time in total.

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Postby nona.m.nona » Fri Dec 18, 2009 12:18 pm

You should probably start by trying to figure out the pattern. What is the rule? (You might not be able to come up with a "formula", but you should be able to come up with what the next few points will be.)

To be a "function", it has to be true that, for any x-value, there will be only one y-value. Two x-values can have the same y-value, but no x-value can go to two or more y-values. Is that true in this case?

For the inverse to be a function, the same has to be true; you'll just have to reverse the x's and y's in all the points. In the original relation, were there any two x-values that shared the same y-value? If not, then there will be no x-values in the inverse (y-values in the original relation) that have the same y-value (x-values in the original relation), so the inverse will be a function.

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