document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025032>Question 1025032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = x^4 + 2x/x^2 &#8722; 1<BR>\n" );
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document.write( "(a) Determine the domain of f. I got x cannot equal 1 and -1<BR>\n" );
document.write( "(b) Determine all zeros of f: i cant find this i set the whole expression to zero and multiplied x^2-1 from both sides leaving me with x^4+2x n ow what do i do?<BR>\n" );
document.write( "(c) Determine all vertical asymptotes of f: this is x= 1 or x=-1<BR>\n" );
document.write( "(d) Determine the y-intercept of f: there is no horizontal asymptotes<BR>\n" );
document.write( "(e) Determine the long range behaviour of f? I don't understand this will you be to please help me.<BR>\n" );
document.write( "Thank you for all your time!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640327 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=640327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Almost assuredly you mean  f(x)=(x^4+2x)/(x^2-1).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E4%2B2x%29%2F%28x%5E2-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E4%2B2x%29%2F%28x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%28x%5E3%2B2%29%29%2F%28%28x-1%29%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28x%28x%5E3%2B2%29%29%2F%28%28x-1%29%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The numerator and denominator have no factor in common.\r<BR>\n" );
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document.write( "Roots and undefined x values will determine intervals on the x-axis.  This affects domain.\r<BR>\n" );
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document.write( "ZEROS<BR>\n" );
document.write( "Look in the numerator.\r<BR>\n" );
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document.write( "x is a zero.<BR>\n" );
document.write( "also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2 ALIGN=MIDDLE  ALT=\"x%5E3%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be a root.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3=-2 ALIGN=MIDDLE  ALT=\"x%5E3=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x=%28-2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=root%283%2C-2%29 ALIGN=MIDDLE  ALT=\"x=root%283%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This root or zero is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-root%283%2C2%29 ALIGN=MIDDLE  ALT=\"x=-root%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "VERTICAL ASYMPTOTES<BR>\n" );
document.write( "These occur at x=1 and x=-1 because f is not defined for those values.  Why?   Because the denominator must never become 0.\r<BR>\n" );
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document.write( "CRITICAL x VALUES<BR>\n" );
document.write( "These are the x values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-root%283%2C2%29 ALIGN=MIDDLE  ALT=\"-root%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -1, 0, 1.\r<BR>\n" );
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document.write( "y-INTERCEPT<BR>\n" );
document.write( "Let x be 0.  What is y?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280%5E4%2B2%2A0%29%2F%280%5E2-1%29 ALIGN=MIDDLE  ALT=\"f%280%29=%280%5E4%2B2%2A0%29%2F%280%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0%2F%28-1%29 ALIGN=MIDDLE  ALT=\"f%280%29=0%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0 ALIGN=MIDDLE  ALT=\"f%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That should all be very helpful for you, although not everything was completed for you. </SPAN>\n" );
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