document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136718>Question 1136718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the rational function f(×)= -4X^2+1/X^2+X-6<BR>\n" );
document.write( "A)Find the vertical asymptote(s),If they exists<BR>\n" );
document.write( "B)Find the horizontal asymptote, if it exists.Dont forget to check for oblique asymptote.<BR>\n" );
document.write( "C)Find the x-intercept of the function.<BR>\n" );
document.write( "D)Find the y-intercept of the function.<BR>\n" );
document.write( "E)sketch the rational function and plot a few points if needed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754528 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Again you should know parentheses are required....<br><BR>\n" );
document.write( "The function is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29+=+%28-%282x%2B1%29%282x-1%29%29%2F%28%28x%2B3%29%28x-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(1) y-intercept: when x=0: -1/6<br><BR>\n" );
document.write( "(2) x-intercept(s): where y=0; i.e., where the numerator is 0: at x=-1/2 and x=1/2<br><BR>\n" );
document.write( "(3) vertical asymptote(s): where the denominator is 0 -- at x=-3 and x=2<br><BR>\n" );
document.write( "(4) horizontal asymptote: y=-4 (degree of numerator and denominator are the same, so ratio of leading coefficients)<br><BR>\n" );
document.write( "A graph of the rational function and the horizontal asymptote:<br><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%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29%2C-4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graph points out another thing you should look for when graphing a rational function: Does the graph cross the horizontal asymptote?<br><BR>\n" );
document.write( "To find out, set the function equal to -4 and solve:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29=-4 ALIGN=MIDDLE  ALT=\"%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x%5E2%2B1+=+-4x%5E2-4x%2B24 ALIGN=MIDDLE  ALT=\"-4x%5E2%2B1+=+-4x%5E2-4x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+23 ALIGN=MIDDLE  ALT=\"4x+=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+23%2F4 ALIGN=MIDDLE  ALT=\"x+=+23%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The graph shows the graph of the rational function crossing the asymptote y=-4 at x= 23/4 = 5.75.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );