document.write( "Question 687897: Find the asymptotes, intercepts, and graph: T(w)= wˆ2+2w+4 over w-1 ??
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Algebra.Com's Answer #425393 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "T(w)=  \r\n" );
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document.write( "Change Y(w) to y and w to x\r\n" );
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document.write( "y = \r\n" );
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document.write( "That has a vertical asymptote.  Set denominator = 0\r\n" );
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document.write( "x-1 = 0\r\n" );
document.write( "  x = 1\r\n" );
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document.write( "So here is the vertical asymptote:\r\n" );
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document.write( "It has no horizontal asymptote because the numerator's largest\r\n" );
document.write( "power of x (its degree) which is 2 is larger that the denominator's largest\r\n" );
document.write( "power of x (its degree) with is 1.  \r\n" );
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document.write( "However since the degree of the numerator is exactly one more\r\n" );
document.write( "than the degree of the denominator, it has a slanted or \"oblique\" asymptote.\r\n" );
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document.write( "We find that by long division:\r\n" );
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document.write( "        x+3\r\n" );
document.write( "x-1)x²+2x+4\r\n" );
document.write( "    x²- x\r\n" );
document.write( "       3x+4\r\n" );
document.write( "       3x-3\r\n" );
document.write( "          7\r\n" );
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document.write( "So y = x+3 + \r\n" );
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document.write( "And the fraction  gets smaller and smaller as x gets\r\n" );
document.write( "larger and larger either positively or negatively, so the curve\r\n" );
document.write( "approaches just being like the line y = x+3 ignoring the remainder\r\n" );
document.write( "or denominator.  So we draw the slant asymptote y = x+3\r\n" );
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document.write( "   \r\n" );
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document.write( "The y-intercept is gotten by substituting x=0\r\n" );
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document.write( "y = \r\n" );
document.write( "y = \r\n" );
document.write( "y = \r\n" );
document.write( "y = -4\r\n" );
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document.write( "So the y-intercept is (0,-4). There is no x-intercept because the numerator\r\n" );
document.write( "is never zero. So we plot the y-intercept and get a few more points, maybe\r\n" );
document.write( "(8,12),(-6,-4), (2,12), (-4,-2.4), (3,9.5), (-1,-1.5). and draw the graph:\r\n" );
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document.write( "Edwin

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