document.write( "Question 1163159: For which of the following equations is y a function of x? Explain how you know.
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\n" ); document.write( "d. 2 • |𝑥| = y
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Algebra.Com's Answer #787160 by ikleyn(52835)\"\" \"About 
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document.write( "(d)  2*|x| = y.\r\n" );
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document.write( "     This formula express y as a function of x\r\n" );
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document.write( "         y = 2*|x|.     (d)\r\n" );
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document.write( "     For every value of x, formula (d) determines y by a unique way.\r\n" );
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document.write( "     In other words, for any real x as an input, formula (d) determines a unique output y.\r\n" );
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document.write( "     By the definition of the notion of a function, it means that formula (d)  determines y as a function of x.\r\n" );
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document.write( "(b)  Same mantra works in case (b).\r\n" );
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document.write( "     You start from the formula\r\n" );
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document.write( "         x^2 + y = 100.\r\n" );
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document.write( "     It defines the expression\r\n" );
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document.write( "         y = 100 - x^2.     (b)\r\n" );
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document.write( "     For every value of x, the formula (b) determines y by a unique way.\r\n" );
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document.write( "     In other words, for any real x as an input, formula (b) determines a unique output y.\r\n" );
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document.write( "     By the definition of the notion of a function, it means that formula (b)  determines y as a function of x.\r\n" );
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document.write( "(a)  Same mantra works in case (a).\r\n" );
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document.write( "     You start from the formula\r\n" );
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document.write( "         x + 5y = 15.\r\n" );
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document.write( "     It defines the expression\r\n" );
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document.write( "         y = \"%2815-x%29%2F5\".     (a)\r\n" );
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document.write( "     For every value of x, formula (a) determines y by a unique way.\r\n" );
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document.write( "     In other words, for any real x as an input, formula (a) determines a unique output y.\r\n" );
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document.write( "\r\n" );
document.write( "     By the definition of the notion of a function, it means that formula (a)  determines y as a function of x.\r\n" );
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document.write( "(c)  Same mantra DOES NOT work in case (c).\r\n" );
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document.write( "     You start from the formula\r\n" );
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document.write( "         x^2 + y^2 = 100.\r\n" );
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document.write( "     It defines the expression\r\n" );
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document.write( "         y = +/- \"sqrt%28100-x%5E2%29\".     (c)\r\n" );
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document.write( "     Formula (c) DOES NOT determine y by a unique way.\r\n" );
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document.write( "     In opposite, to each value of x  between -10 and 10,  -10 < x < 10,  formula (c) determines TWO values of y.\r\n" );
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document.write( "     In other words, for any real x as an input, formula (c) determines TWO DIFFERENT outputs y.\r\n" );
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document.write( "     By the definition of the notion of a function, it means that formula (c)  DOES NOT determine y as a function of x.\r\n" );
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document.write( "     In this case, y is not a function of x.\r\n" );
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