document.write( "Question 995537: True or False
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document.write( "The rule y^2 = x^3 defines a function.\r
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Algebra.Com's Answer #614270 by Theo(13342)![]() ![]() You can put this solution on YOUR website! i would say false.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "y^2 = x^3 is solved as follows:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "take the square root of both sides to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "y = plus or minus sqrt(x^3)\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "that plus or minus tell you that you have more than one value of y for each value of x.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "for example:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "assume that x = 4.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you have y^2 = x^3 which means that y^2 = 64 when x is 4 because 4^3 = 64.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "take the square root of both sides of that equation to get y = +/- 8.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "for the value of x = 4, you can get y = + 8 or - 8.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "more than one value of y for a given value of x means that you do not have a function since that violates the rules of a function that state that there is one and only one value of y for each and every value of x.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "there may be only one possible value of y^2, but there are more than one possible value of y.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |