document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112972>Question 112972</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072424281/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> My teacher would like us to graph, including any oblique asymptotes, y= f(x) = X^2+5<BR>\n" );
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document.write( "x+1\r<BR>\n" );
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document.write( "find intercepts, verticle asymptotes, and horizontal asymptotes. I have the graph done, I just need to know how to do the written work.<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82297 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given expression is: y = f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2+%2B+5%29%2F%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"+%28x%5E2+%2B+5%29%2F%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The intercepts are given as follows:  \r<BR>\n" );
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document.write( "Y - intercept put x = 0  \r<BR>\n" );
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document.write( "==> y = (0 + 5)/(0 + 1) \r<BR>\n" );
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document.write( "==> y = 5/1 \r<BR>\n" );
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document.write( "==> y = 5 \r<BR>\n" );
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document.write( "The x-intercepts are given when y = 0  \r<BR>\n" );
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document.write( "==> 0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+5%29%2F%28x+%2B+1%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+5%29%2F%28x+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> 0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "==> x^2 = - 5 \r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+i%28sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"+x+=+i%28sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (+ -) \r<BR>\n" );
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document.write( "The graph looks this way: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-15%2C+15%2C+-15%2C+15%2C+%28x%5E2+%2B+5%29%2F%28x+%2B+1%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-15%2C+15%2C+-15%2C+15%2C+%28x%5E2+%2B+5%29%2F%28x+%2B+1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "The vertical and the horizontal asymptotes are found as follows: \r<BR>\n" );
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document.write( "The vertical asymptotes come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.\r<BR>\n" );
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document.write( "x + 1 = 0 \r<BR>\n" );
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document.write( "==> x = -1 \r<BR>\n" );
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document.write( "Thus the vertical asymptotes.\r<BR>\n" );
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document.write( "Since the degree of the numerator is one greater than the degree of the denominator, I'll have a slant asymptote (not a horizontal one), and I'll find the slant asymptote by long division.\r<BR>\n" );
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document.write( "Thus by long dision we find that y = x + 1 is the slant asymptote for the given equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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