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Real-Life Applications of Relations Versus Functions and Reversal of Variables

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Where in the real world might be a situation arise where it would be preferable for data to form a relation but not a function? Please explain it to me in detail - thanks!

If the varibles in an equation were reversed, what would happen to the graph of the equation? Here's an example of what I'm asking: how would the graph of
y=x^2 relate to the graph x = y^2? When might this reversal of variables be useful in the real world?

Any and all help you can give will be greatly appreciated.

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Real-Life Applications of Relations Versus Functions and Reversal of Variables are discussed. The solution is detailed and well presented.

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