document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615579>Question 615579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> draw asymptotes  (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387244 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=387244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2<BR>\n" );
document.write( "**<BR>\n" );
document.write( "I don't have the means to plot a graph for you, but I can provide information with which you can plot the curve yourself.<BR>\n" );
document.write( "When degree of numerator is one unit higher than that of the denominator, you will have slant or oblique asymptotes, as in this case.<BR>\n" );
document.write( "To find equation of slant asymptote, divide numerator by denominator by long division or synthetic division. The quotient is the equation of the slant asymptote.<BR>\n" );
document.write( "(x^2+5x+5)/(x+2)=(x+3)+remainder=1<BR>\n" );
document.write( "equation of slant asymptote: y=x+3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "To find vertical asymptote, set denominator=0, then solve for x<BR>\n" );
document.write( "x+2=0<BR>\n" );
document.write( "x=-2=vertical asymptote<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y-intercept<BR>\n" );
document.write( "set x=0,then solve for y<BR>\n" );
document.write( "f(0)=(x^2+5x+5)/(x+2)=5/2<BR>\n" );
document.write( "y-intercept=5/2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x-intercepts<BR>\n" );
document.write( "set y=0<BR>\n" );
document.write( "x^2+5x+5=0<BR>\n" );
document.write( "solve by quadratic formula:<BR>\n" );
document.write( "x=-3.62 and -1.38<BR>\n" );
document.write( "..<BR>\n" );
document.write( "number line<BR>\n" );
document.write( "<....-.....-3.62...+...-2...-...-1.38...+....><BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%28x%5E2%2B5x%2B5%29%2F%28x%2B2%29%2Cx%2B3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );