document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278070>Question 278070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for a function that is the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=1%2Fx%5E3+ ALIGN=MIDDLE  ALT=\"+y=1%2Fx%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > reflected through the y-axis and shifted down 3 units </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202378 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for a function that is the graph of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Fx%5E3 ALIGN=MIDDLE  ALT=\"y=1%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > reflected through the y-axis and shifted down 3 units,\r<BR>\n" );
document.write( "\n" );
document.write( "We start with the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Fx%5E3 ALIGN=MIDDLE  ALT=\"y=1%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C1%2Fx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C1%2Fx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "It has the x and the y-axis as asymptotes\r<BR>\n" );
document.write( "\n" );
document.write( "Then we reflect it through the y-axis by replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2Fx%5E3 ALIGN=MIDDLE  ALT=\"y=1%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F%28-x%29%5E3 ALIGN=MIDDLE  ALT=\"y=1%2F%28-x%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "which simplifies to:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2Fx%5E3 ALIGN=MIDDLE  ALT=\"y=-1%2Fx%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This gives the graph below\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C-1%2Fx%5E3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C-1%2Fx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "with the same two asymptotes.\r<BR>\n" );
document.write( "\n" );
document.write( "Finally we shift it down 3 units by subtracting 3 from the<BR>\n" );
document.write( "right side, which gives the equation\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2Fx%5E3-3 ALIGN=MIDDLE  ALT=\"y=-1%2Fx%5E3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >}\r<BR>\n" );
document.write( "\n" );
document.write( "and the graph is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C-1%2Fx%5E3-3%2C-3sqrt%28sin%285x%29%29%2Fsqrt%28sin%285x%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The blue dotted line is the asymptote.  The original curve had<BR>\n" );
document.write( "the x-axis and y-axis as its asymptotes, and this new graph has the line y=-3 as its horizontal asymptote, and has the y-axis as its vertical asymptote..\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );