Algebra.Com's Answer #185790 by Edwin McCravy(20056)![\"\"](\"/images/stars/stars-13.gif\")  
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Write the rule that represents the function
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document.write( "x = -1, 0, 1, 2
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document.write( "y = 1/4, 1, 4, 16
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document.write( "There are infinitely many rules that would represent that,\r\n" );
document.write( "but the most obvious one is\r\n" );
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document.write( "because  ,  ,  ,  \r\n" );
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document.write( "But don't allow your teacher to tell you that is the ONLY one!\r\n" );
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document.write( "For we can always find a nth-degree polynomial that will go through\r\n" );
document.write( "any n-1 points.\r\n" );
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document.write( "For instance this answer \r\n" );
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document.write( "is just as good, although\r\n" );
document.write( "not quite as simple:\r\n" );
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document.write( "Substitute those x-values in that and you will also get the y-values.\r\n" );
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document.write( "-------------------------\r\n" );
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document.write( "Write the rule that represents the function \r\n" );
document.write( "x = 0, 1, 2, 3, 4\r\n" );
document.write( "y = -7, -2, 3, 8, 13\r\n" );
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document.write( "We notice that \r\n" );
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document.write( "-7+5=-2, -2+5=3, 3+5=8, 8+5=13\r\n" );
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document.write( "So we suspect that this is linear, of the form y=mx+b\r\n" );
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document.write( "So we try \r\n" );
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document.write( "y=mx+b\r\n" );
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document.write( "Substitute (0,-7)\r\n" );
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document.write( "-7=m(0)+b\r\n" );
document.write( "-7=b\r\n" );
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document.write( "So y=mx-7\r\n" );
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document.write( "Substitute (1,-2)\r\n" );
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document.write( "-2=m(1)-7\r\n" );
document.write( "-2=m-7\r\n" );
document.write( "5=m\r\n" );
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document.write( "so the obvious answer is y=5x-7\r\n" );
document.write( "and if you substitute all those s-values you'll get\r\n" );
document.write( "the corresponding y-values.\r\n" );
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document.write( "But there are many other functions that work too.\r\n" );
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document.write( "Edwin \n" );
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