document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=585599>Question 585599</A>: <I><SPAN STYLE=\"word-break: break-all;\">  f(x)= x^2-4x+4/x-1<BR>\n" );
document.write( "a)	Identify the x & y-intercepts <BR>\n" );
document.write( "b)	Find all vertical, horizontal and slant asymptotes <BR>\n" );
document.write( "c)	Check for symmetry <BR>\n" );
document.write( "d)	Plot sufficient solution points<BR>\n" );
document.write( "e)	Sketch the graph of  f(x)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373415 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=373415\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)= (x^2-4x+4)/(x-1)<BR>\n" );
document.write( "a) Identify the x & y-intercepts<BR>\n" );
document.write( "x-intercept ?<BR>\n" );
document.write( "Let y = 0; then x^2-4x+4 = (x-2)^2 = 0<BR>\n" );
document.write( "x = 2 is the x-intercept.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "y-intercept ?<BR>\n" );
document.write( "Let x = 0, then y = 4/(-1) = -4<BR>\n" );
document.write( "------------------------------- <BR>\n" );
document.write( "b) Find all vertical, horizontal and slant asymptotes<BR>\n" );
document.write( "Vertical with x = 1<BR>\n" );
document.write( "Horizontal with y = x^2/0x^2 is undefined.<BR>\n" );
document.write( "So no horizontal asymptote.<BR>\n" );
document.write( "Slant: (x^2-4x+4)/(x-1) = (x-3)(x-1)+1<BR>\n" );
document.write( "Slant asymptote: y = x-3<BR>\n" );
document.write( "----------------------------------- <BR>\n" );
document.write( "c) Check for symmetry<BR>\n" );
document.write( "f(-x) = (x^2+4x+4)/(-x-1)<BR>\n" );
document.write( "-f(-x) = (x^2+4x+4)/(x+1)<BR>\n" );
document.write( "Since f(x) is not equal to f(-x), no y-axis symmetry.<BR>\n" );
document.write( "Since f(x) is not equal to -f(-x), no origin symmetry.<BR>\n" );
document.write( "------------------------------------- <BR>\n" );
document.write( "d) Plot sufficient solution points<BR>\n" );
document.write( "e) Sketch the graph of f(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%5E2-4x%2B4%29%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%5E2-4x%2B4%29%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );