Algebra.Com's Answer #845117 by ikleyn(52803)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "State whether or not the given equations determines y as a function of x
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document.write( "(1) X+Y=1
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document.write( "(2) X^2 + y^2=1
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document.write( "(3) Y^2=X^2
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document.write( "(4) Y=√x
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document.write( "(5) Y=+-√X
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document.write( "(1) From x + y = 1, we have an equivalent equation\r\n" );
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document.write( " y = 1-x.\r\n" );
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document.write( " It determines \"y\" by an unique way via x. So, (1) determines \"y\" as a function of x.\r\n" );
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document.write( "(2) From  +  = 1, we have an equivalent expression\r\n" );
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document.write( " y = +/-  .\r\n" );
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document.write( " It determines two values of \"y\" for each value of x. So, (2) does not determine \"y\" as a function of x.\r\n" );
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document.write( "(3) From = , we have an equivalent expression\r\n" );
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document.write( " y = +/- |x|.\r\n" );
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document.write( " It determines two values of \"y\" for each value of x. So, (3) does not determine \"y\" as a function of x.\r\n" );
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document.write( "(4) y =  determines a unique value of \"y\" for each positive value of x. \r\n" );
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document.write( " So, (4) determines \"y\" as a function of x.\r\n" );
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document.write( "(5) y = +/- determines two value of \"y\" for each positive value of x. \r\n" );
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document.write( " So, (5) does not determine \"y\" as a function of x.\r\n" );
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document.write( "Solved.\r
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document.write( "All questions are answered, with complete explanations.\r
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