document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103413>Question 103413</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131430734/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have the following problem. I will be honest, it is for homework, so the answer is not in the back of the book. I am just trying to understand how to properly solve it.\r<BR>\n" );
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document.write( "y = (x^2 - 4)/2x^4\r<BR>\n" );
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document.write( "I tried to simplify this on the website and it gave me y - (x^2 - 4)/2x^4 = 0\r<BR>\n" );
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document.write( "I am suppose to state what the intercept is and what it is symmetric to (y-axis, x-axis and/or origin)\r<BR>\n" );
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document.write( "Here is what I did.\r<BR>\n" );
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document.write( "y = (x^2 - 4)/2x^4<BR>\n" );
document.write( "y = (x^2 - 4)/(x^2)(2x^2) - I broke apart the 2x^4<BR>\n" );
document.write( "y = -4/2x^2   - I thought the x^2 on the bottom of the fraction cancelled out the top.<BR>\n" );
document.write( "After that, I did not know what else to do. I could multiply both sides by 2x^2, but that did not seem to get me anywhere, so I started by making a list of the possible values of x and y.\r<BR>\n" );
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document.write( "Here is what I came up with.<BR>\n" );
document.write( "x = 2, y = -1/2<BR>\n" );
document.write( "x = -2, y = -1/2<BR>\n" );
document.write( "x = 1, y = -2\r<BR>\n" );
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document.write( "I plotted these and my answer was the following:<BR>\n" );
document.write( "1. I could not find an intercept. I don't see where either can equal 0, unless they both equal 0.<BR>\n" );
document.write( "2. They would be symmetric to the y-axis.\r<BR>\n" );
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document.write( "Am I correct? My main goal is to find out what else to do with the equation. I'm lost.\r<BR>\n" );
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document.write( "Thanks for your help in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75216 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=75216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2+-+4%29%2F2x%5E4 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2+-+4%29%2F2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2+-+4%29%2F%28x%5E2%29%282x%5E2%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2+-+4%29%2F%28x%5E2%29%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - I broke apart the 2x^4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4%2F2x%5E2 ALIGN=MIDDLE  ALT=\"y+=+-4%2F2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - I thought the x^2 on the bottom of the fraction cancelled out the top.<BR>\n" );
document.write( "You're on the right track but you lost some terms. <BR>\n" );
document.write( "Let's back up.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2+-+4%29%2F2x%5E4 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2+-+4%29%2F2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2F2x%5E4+-+4%2F2x%5E4 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2F2x%5E4+-+4%2F2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1%2F2x%5E2+-+4%2F2x%5E4 ALIGN=MIDDLE  ALT=\"y+=+1%2F2x%5E2+-+4%2F2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I don't think doing the division gives you any more insight. I think it's better to go back the your original form. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%5E2+-+4%29%2F2x%5E4 ALIGN=MIDDLE  ALT=\"y+=+%28x%5E2+-+4%29%2F2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "First off, where does this equation equal zero. The most obvious place is when the numerator equals zero. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+4=0 ALIGN=MIDDLE  ALT=\"x%5E2+-+4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+4 ALIGN=MIDDLE  ALT=\"x%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=2 and x=-2 are both points where y=0.<BR>\n" );
document.write( "To check for symmetry, do as you did before. <BR>\n" );
document.write( "Try a number and its negative and see what you get for a result. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%281%29+=+%281%5E2+-+4%29%2F2%281%29%5E4 ALIGN=MIDDLE  ALT=\"y%281%29+=+%281%5E2+-+4%29%2F2%281%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%281%29+=+-3%2F2 ALIGN=MIDDLE  ALT=\"y%281%29+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28-1%29+=+%28%28-1%29%5E2-4%29%2F2%28-1%29%5E4 ALIGN=MIDDLE  ALT=\"y%28-1%29+=+%28%28-1%29%5E2-4%29%2F2%28-1%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28-1%29+=+-3%2F2 ALIGN=MIDDLE  ALT=\"y%28-1%29+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you look at the equation you are squaring x and squaring the square of x. Working with squares of negatives and positives will give you the same answer so you graph will be symmetric about the y axis. <BR>\n" );
document.write( "You can also graph some points and look at the graph. <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+%28x%5E2+-+4%29%2F2x%5E4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+5%2C+%28x%5E2+-+4%29%2F2x%5E4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "As you can see, the graph plummets as x or -x approaches 0 because <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E0%2C%28y%29%29=-infinity%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E0%2C%28y%29%29=-infinity%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After you pass x=2 in the positive sense and x=-2 in the negative sense, you have a slight increase above zero and then quickly approach zero as x gets larger. There is a maximum value of y=0.0312 at x=+/-2.8 and then quickly head towards zero. Easiest way to see this is to use EXCEL to calculate a bunch of x,y points (use one column for your x values and then the next column use a formula for your y values). Then you can graph that also. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+1%2C+5%2C+-1%2C+1%2C+%28x%5E2+-+4%29%2F2x%5E4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+1%2C+5%2C+-1%2C+1%2C+%28x%5E2+-+4%29%2F2x%5E4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Additionally from your graph and from looking at the values you see that: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3Einfinity%2C%28y%29%29=0%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3Einfinity%2C%28y%29%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E-infinity%2C%28y%29%29=0%29 ALIGN=MIDDLE  ALT=\"lim%28x-%3E-infinity%2C%28y%29%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Hope it helps. Good Luck! </SPAN>\n" );
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