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You can put this solution on YOUR website!
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document.write( "There is a fallacy in mathematics, and that is that (3,8) can stand either\r\n" );
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document.write( "(1) the point with x-coordinate 3 and y-coordinate 8. \r\n" );
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document.write( "or\r\n" );
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document.write( "(2) the open interval {x|3 < x < 8}\r\n" );
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document.write( "----------------o==============o---------> \r\n" );
document.write( "-2 -1 0 1 2 3 4 5 6 7 8 9 10 11\r\n" );
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document.write( "Try not to get these confused.\r\n" );
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document.write( "Draw all three lines y=2x+5, y=-3, and y=5x\r\n" );
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document.write( "The red line is y=2x+5. Chop it off on the left\r\n" );
document.write( "at (-3,-1), and put a closed circle on the left end\r\n" );
document.write( "and an open circle on the right end at (0,5)\r\n" );
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document.write( "The green line is y=-3. Chop it off both on the left\r\n" );
document.write( "and right at (-3,0), and put a closed circle at\r\n" );
document.write( "(-3,0). There will be just one single green point \r\n" );
document.write( "at (-3,0), because the green line is chopped off on\r\n" );
document.write( "both sides of that one green point.\r\n" );
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document.write( "The blue line is y=-5x. Chop it off on the left\r\n" );
document.write( "at (0,0), and put a open circle on the left end\r\n" );
document.write( "and let it extend indefinitely on the right.\r\n" );
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document.write( "A. Find domain and range.\r\n" );
document.write( "Look at the graph above:\r\n" );
document.write( "The left most point is (-3,-1), so x starts the domain at -3. \r\n" );
document.write( "All the x values to the right of -3 have a y-value, so the\r\n" );
document.write( "domain is [-3,∞ )\r\n" );
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document.write( "The highest point is (0,5), but it does not include that point,\r\n" );
document.write( "but it includes all lower values of y, so the range is (-∞,5). \r\n" );
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document.write( "B. Locate intercepts.\r\n" );
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document.write( "It has only one intercept, an x-intercept on the left part y=x+5\r\n" );
document.write( "Substitute y=0 and get 0=2x+5, or 2x=-5, or x=-5/2=-2.5. So the only \r\n" );
document.write( "intercept is (-2.5,0). [Notice that both endpoints on the y-axis\r\n" );
document.write( "are not included. So there is not another x-intercept and no \r\n" );
document.write( "y-intercept at all.\r\n" );
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document.write( "C. Is f continuous on its domain?\r\n" );
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document.write( "No because the pieces do not connect. To be continuous on the domain\r\n" );
document.write( "each part must begin at the same point where the preceding part ends. \r\n" );
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document.write( "Edwin \n" );
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