why would you use the horizontal line test and vertical line test? y=x^2 is not one to one in the horizontal line test but it is one to one using the vertical line test?

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Tony - If the horizontal line test "fails", then the function can not have an inverse (at least for that domain). If you graph a function y=x^2 for the domain x>0, then it DOES pass the vertical line test and under that restricted constraint x>0 it has a valid inverse. The vertical line test, as you probably know, tests if the graph is a "function". Hope that helps!