document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435117>Question 435117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> F(x)= (x-1)/(x²-4)<BR>\n" );
document.write( "Find the domain of f(x).<BR>\n" );
document.write( "Describe the horizontal and vertical asymptotes and any symmetry of the graph of f(x).<BR>\n" );
document.write( "Find the x and y intercepts.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301251 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factoring the denominator gives us:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%29%2F%28x%2B2%29%28x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%29%2F%28x%2B2%29%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The domain is the set of all x-values for which the function is defined.<BR>\n" );
document.write( "The function is undefined for values of x which make the denominator equal to zero.<BR>\n" );
document.write( "The function is undefined at x = -2, 2.<BR>\n" );
document.write( "So the domain of f(x) is (-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,-2) U (-2,2) U (2,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "The vertical asymptotes are x = -2 and x = 2.<BR>\n" );
document.write( "The horizontal asymptote is y = 0, since for large positive and negative values of x, <BR>\n" );
document.write( "the function approaches but never reaches zero.<BR>\n" );
document.write( "The x-intercept is the value of the function when y=0. So the x-intercept is x=1.<BR>\n" );
document.write( "The y-intercept is obtained by evaluating the function at x=0<BR>\n" );
document.write( "f(0) = -1/-4 = 1/4<BR>\n" );
document.write( "So the y-intercept is y= 1/4<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%2C%28x-1%29%2F%28%28x%2B2%29%28x-2%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x-1%29%2F%28%28x%2B2%29%28x-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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