document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157588>Question 1157588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this....Find the​ vertical, horizontal, and oblique​ asymptotes, if​ any, for the given rational function.<BR>\n" );
document.write( "Q(x)=(3x^2-11x-4)/(2x^2-7x-4)<BR>\n" );
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document.write( "(1) Horizontal or oblique asymptotes<br><BR>\n" );
document.write( "The degrees of the numerator and denominator are the same, so there is a horizontal asymptote and no oblique asymptote.<br><BR>\n" );
document.write( "The ratio of the leading coefficients gives you the horizontal asymptote.<br><BR>\n" );
document.write( "ANSWER: Horizontal asymptote at y = 3/2.<br><BR>\n" );
document.write( "(2) Vertical asymptotes<br><BR>\n" );
document.write( "Vertical asymptotes will occur wherever there is a linear factor in the denominator that is not also in the numerator.<br><BR>\n" );
document.write( "Factor numerator and denominator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283x%2B1%29%28x-4%29%29%2F%28%282x%2B1%29%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28%283x%2B1%29%28x-4%29%29%2F%28%282x%2B1%29%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There is a vertical asymptote were the factor (2x+1) in the denominator is equal to 0.<br><BR>\n" );
document.write( "ANSWER: There is a single vertical asymptote, at x = -1/2.<br><BR>\n" );
document.write( "What about the factors (x-4) in both numerator and denominator?<br><BR>\n" );
document.write( "For x=4, the denominator is 0 and so the function is undefined.  For all other values of x, the function is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B1%29%2F%282x%2B1%29 ALIGN=MIDDLE  ALT=\"%283x%2B1%29%2F%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the graph of the given function is the same as the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B1%29%2F%282x%2B1%29 ALIGN=MIDDLE  ALT=\"3x%2B1%29%2F%282x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > except that there is a hole in the graph at x=4.<br><BR>\n" );
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