document.write( "Question 156036: y=x-1 [over] x+4. Find the x and y intercepts along with the asymptotes. Sketch tehe graph. Please help me, I really have no idea what to do with rational functions!!! \n" ); document.write( "
Algebra.Com's Answer #115075 by Edwin McCravy(20059) $\"\"$ $\"About$
You can put this solution on YOUR website!
$\"y=%28x-1%29%2F%28x%2B4%29\"$ . Find the x and y intercepts along with the asymptotes. Sketch the graph. Please help me, I really have no idea what to do with rational functions!!!
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document.write( "First find the equation of vertical asymptote(s), if any, \r\n" );
document.write( "by setting the denominator equal to zero:\r\n" );
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document.write( "So  is the equation of the vertical asymptote.\r\n" );
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document.write( "Let's draw that vertical asymptote:\r\n" );
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document.write( "Now let's find the horizontal asymptotes by whichever of\r\n" );
document.write( "these rules applies:\r\n" );
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document.write( "Rules for horizontal asymptotes:\r\n" );
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document.write( "1. If the largest exponent of x in the numerator is GREATER than the\r\n" );
document.write( "largest exponent of x in the denominator, there is \r\n" );
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document.write( "2. If the largest exponent of x in the numerator is LESS than the\r\n" );
document.write( "largest exponent of x in the denominator, the horizontal asymptote is the\r\n" );
document.write( "x-axis, whose equation is \r\n" );
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document.write( "3. If the largest exponent of x in the numerator is EQUAL to the\r\n" );
document.write( "largest exponent of x in the denominator, the horizontal asymptote is \r\n" );
document.write( "horizontal line whose equation is\r\n" );
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document.write( "  \r\n" );
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document.write( "---------------------\r\n" );
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document.write( " or\r\n" );
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document.write( ". \r\n" );
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document.write( "The largest exponent of x in the numerator is 1, and the\r\n" );
document.write( "largest exponent in the denominator is also 1, so they are\r\n" );
document.write( "equal.  So we use rule 3.  The coefficients are both 1.\r\n" );
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document.write( "so the equation of the horizontal asymptote is\r\n" );
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document.write( " or\r\n" );
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document.write( "So we draw the horizontal asymptote on the same set of axes:\r\n" );
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document.write( "Next we get a point on each side of the vertical\r\n" );
document.write( "asymptote:\r\n" );
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document.write( "Choose x=-5 to get a point on the left side of the\r\n" );
document.write( "vertical asymptote:\r\n" );
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document.write( "  \r\n" );
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document.write( "So a point on the left side of the vertical asymptote\r\n" );
document.write( "is (-5,6)\r\n" );
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document.write( "Let's plot that point:\r\n" );
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document.write( "Now we'll sketch in a curve on the left side of that \r\n" );
document.write( "vertical asymptote that goes through that point and \r\n" );
document.write( "that also gets closer and closer to both the vertical \r\n" );
document.write( "and the horizontal asymptote, like this:\r\n" );
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document.write( "Choose x=-3 to get a point on the right side of the\r\n" );
document.write( "vertical asymptote:\r\n" );
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document.write( "  \r\n" );
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document.write( "So a point on the right side of the vertical asymptote\r\n" );
document.write( "is (-3,-4)\r\n" );
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document.write( "Let's plot that point too:\r\n" );
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document.write( "Now we'll sketch in a curve on the right of the vertical\r\n" );
document.write( "asymptote that goes through that point and  that also gets \r\n" );
document.write( "closer and closer to both the vertical and the horizontal \r\n" );
document.write( "asymptote, like this:\r\n" );
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document.write( "That's it!  It has two parts, one on each side of the\r\n" );
document.write( "vertical asymptotes.  \r\n" );
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document.write( "Oh, I almost forgot.  You wanted the x and y intercepts, too.\r\n" );
document.write( "We didn't need them at all for the graph, but we'll get them.\r\n" );
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document.write( "To get the x-intercept, let\r\n" );
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document.write( "Multiply both sides by \r\n" );
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document.write( "So the x-intercept is (1,0).\r\n" );
document.write( "That's where the curve crosses the x-axis,\r\n" );
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document.write( "To get the y-intercept, let\r\n" );
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document.write( "So the y-intercept is (0,).\r\n" );
document.write( "That's where the curve crosses the y-axis,\r\n" );
document.write( "just a tad below the origin. In this case,\r\n" );
document.write( "they don't help us much with the graph,\r\n" );
document.write( "but in some problems they do.\r\n" );
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document.write( "(In some problems, you have two or more\r\n" );
document.write( "vertical asymptotes, so in those, you get \r\n" );
document.write( "points in between them as well as on each\r\n" );
document.write( "side of them).\r\n" );
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document.write( "Edwin
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