document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204539>Question 1204539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the Rational Function f(x)= p(x)/q(x), which of the following statements are true? Check all that apply.\r<BR>\n" );
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document.write( "a. If q(x) has a higher degree term than p(x) then the Horizontal Asymptote is y=0\r<BR>\n" );
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document.write( "b. If the highest degree term in p(x) is greater than the highest degree term in q(x) there will be more than one Horizontal Asymptote\r<BR>\n" );
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document.write( "c. If the highest degree term of p(x) is the same as the highest degree term of q(x) then the Horizontal Asymptote is x=0\r<BR>\n" );
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document.write( "d. If f(x) has a HORIZONTAL ASYMPTOTE y=a, then as the input values increase or decrease without bound, the output values will approach a\r<BR>\n" );
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document.write( "e. The Horizontal Asymptote is a guiding line for the function as the input values increase or decrease without bound </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840854 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the Rational Function f(x)= p(x)/q(x), which of the following statements are true? Check all that apply.\r<BR>\n" );
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document.write( "Asymptotes<BR>\n" );
document.write( "A vertical asymptote of a graph is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.\r<BR>\n" );
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document.write( "<font color=red>recall</font>:\r<BR>\n" );
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document.write( "If<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N ALIGN=MIDDLE  ALT=\"+N\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the degree of the numerator and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+ ALIGN=MIDDLE  ALT=\"D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the degree of the denominator, and\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+%3C+D ALIGN=MIDDLE  ALT=\"N+%3C+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=+D ALIGN=MIDDLE  ALT=\"N+=+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ratio of the leading coefficients.<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+%3E+D ALIGN=MIDDLE  ALT=\"N+%3E+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > horizontal asymptote.<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+%3E+D%2B1 ALIGN=MIDDLE  ALT=\"N+%3E+D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( the degree of numerator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than the degree of the denominator) ,then there is slant asymptote \r<BR>\n" );
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document.write( "A horizontal asymptote of a graph is a horizontal line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+b ALIGN=MIDDLE  ALT=\"y+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the graph approaches the line as the inputs approach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "A slant asymptote of a graph is a slanted line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b+ ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >where the graph approaches the line as the inputs approach <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "a. If q(x) has a higher degree term than p(x) then the Horizontal Asymptote is y=0\r<BR>\n" );
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document.write( "<font color=red>True</font>\r<BR>\n" );
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document.write( "reason:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+%3C+D ALIGN=MIDDLE  ALT=\"N+%3C+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. If the highest degree term in p(x) is greater than the highest degree term in q(x) there will be more than one Horizontal Asymptote\r<BR>\n" );
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document.write( "<font color=red>False</font>\r<BR>\n" );
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document.write( "reason:<BR>\n" );
document.write( "if<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+%3E+D ALIGN=MIDDLE  ALT=\"+N+%3E+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no+ ALIGN=MIDDLE  ALT=\"no+\"   DISABLED_style= \"max-width:90%; height:auto;\" >horizontal asymptote.\r<BR>\n" );
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document.write( "c. If the highest degree term of p(x) is the same as the highest degree term of q(x) then the Horizontal Asymptote is x=0\r<BR>\n" );
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document.write( "<font color=red>False</font>\r<BR>\n" );
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document.write( "reason:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=D ALIGN=MIDDLE  ALT=\"+N+=D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ratio of leading coefficients\r<BR>\n" );
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document.write( "d. If f(x) has a HORIZONTAL ASYMPTOTE y=a, then as the input values increase or decrease without bound, the output values will approach a.\r<BR>\n" );
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document.write( "<font color=red>True</font>\r<BR>\n" );
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document.write( "example\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%286x-1%29%2F%283x%2B7%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%286x-1%29%2F%283x%2B7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > horizontal asymptote of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+x+-+1%29%2F%283+x+%2B+7%29-%3E2 ALIGN=MIDDLE  ALT=\"%286+x+-+1%29%2F%283+x+%2B+7%29-%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e. The Horizontal Asymptote is a guiding line for the function as the input values increase or decrease without bound\r<BR>\n" );
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document.write( "<font color=red>True</font>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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