document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866602>Question 866602</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to figure out how to describe the graph of the equation y= 4/x + 1. Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522404 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The expected description is whatever you were taught in your math class, and we do not know what that was.<BR>\n" );
document.write( "Also, I am not sure if you really mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=+4%2Fx+%2B+1%29 ALIGN=MIDDLE  ALT=\"green%28y=+4%2Fx+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you wrote,<BR>\n" );
document.write( "or if you really meant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=4%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"blue%28y=4%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which should be written as y=4/(x+1).<BR>\n" );
document.write( "Either function is derived from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=1%2Fx%29 ALIGN=MIDDLE  ALT=\"red%28y=1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "translated and dilated vertically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C1%2Fx%2C4%2Fx+%2B+1%2C4%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C1%2Fx%2C4%2Fx+%2B+1%2C4%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If you are studying functions and their graphs:<BR>\n" );
document.write( "you would be expected to say that there is a vertical asymptote, and a horizontal asymptote.<BR>\n" );
document.write( "The vertical asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=+4%2Fx+%2B+1%29 ALIGN=MIDDLE  ALT=\"green%28y=+4%2Fx+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=1%2Fx%29 ALIGN=MIDDLE  ALT=\"red%28y=1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1=0 ALIGN=MIDDLE  ALT=\"x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=4%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"blue%28y=4%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "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;\" > for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=4%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"blue%28y=4%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28y=1%2Fx%29 ALIGN=MIDDLE  ALT=\"red%28y=1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=+4%2Fx+%2B+1%29 ALIGN=MIDDLE  ALT=\"green%28y=+4%2Fx+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You may be expected to say more about the function, but there are many possibilities, and I may not think if every one.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you are studying conic sections:<BR>\n" );
document.write( "you may be expected to sat that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Fx ALIGN=MIDDLE  ALT=\"y=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=1 ALIGN=MIDDLE  ALT=\"xy=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > graphs as a hyperbola,<BR>\n" );
document.write( "with the transverse axis along the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x ALIGN=MIDDLE  ALT=\"y=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The graphs of the other functions,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=blue%28y=4%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"blue%28y=4%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28y=+4%2Fx+%2B+1%29 ALIGN=MIDDLE  ALT=\"green%28y=+4%2Fx+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "are also hyperbolas. </SPAN>\n" );
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