document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194757>Question 1194757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the function f(x)=2+1/(x-1)\r<BR>\n" );
document.write( "\n" );
document.write( "1. Rewrite this function as a single fraction over the denominator i.\r<BR>\n" );
document.write( "\n" );
document.write( "2. Find the domain of this hyperbola \r<BR>\n" );
document.write( "\n" );
document.write( "3. Explain, in complete sentences, how you use this information to determine the vertical asymptote for this function. Then write the equation of the vertical asymptote. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827013 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=827013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2B1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%2B1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "1. Rewrite this function as a single fraction over the denominator i.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2%2B1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=2%2B1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%282%28x-1%29%29%2F%28x-1%29%2B1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%282%28x-1%29%29%2F%28x-1%29%2B1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%282x-2%29%2F%28x-1%29%2B1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%282x-2%29%2F%28x-1%29%2B1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%282x-2%2B1%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%282x-2%2B1%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%282x-1%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%282x-1%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. Find the domain of this hyperbola\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "domain: all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > except that makes denominator equal to zero\r<BR>\n" );
document.write( "\n" );
document.write( "that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29=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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, domain is: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3. Explain, in complete sentences, how you use this information to determine the vertical asymptote for this function. Then write the equation of the vertical asymptote.\r<BR>\n" );
document.write( "\n" );
document.write( "For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator, of the simplified function. So, in your case, the vertical asymptote is <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;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%0D%0Agreen%28line%281%2C-10%2C1%2C10%29%29%2C%0D%0A%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%282x-1%29%2F%28x-1%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );