document.write( "Question 64954: f(x)= x2-9over x2-5x-14 \n" ); document.write( "
Algebra.Com's Answer #45445 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "           xｲ - 9\r\n" );
document.write( "f(x) = 覧覧覧覧覧覧覧\r\n" );
document.write( "        xｲ - 5x - 14\r\n" );
document.write( "\r\n" );
document.write( "So? What do you want us to do with it?  You forgot to give us\r\n" );
document.write( "any instructions. Next time you post a problem, be sure to\r\n" );
document.write( "give the instructions as to what is supposed to be done.  Don't\r\n" );
document.write( "just give the equation or expression without telling us what to\r\n" );
document.write( "do with it.  Otherwise all we can do is guess.\r\n" );
document.write( "\r\n" );
document.write( "Do you want to find all the vertical and horizontal asymptotes,\r\n" );
document.write( "find the domain and range and draw the graph?  I'll guess that's \r\n" );
document.write( "what you want.\r\n" );
document.write( "\r\n" );
document.write( "To find the equations of the vertical asymptotes by setting the \r\n" );
document.write( "denominator = 0 and solving for x:\r\n" );
document.write( "\r\n" );
document.write( "  xｲ - 5x - 14 = 0\r\n" );
document.write( "(x - 7)(x + 2) = 0\r\n" );
document.write( "\r\n" );
document.write( "Setting x-7=0 gives x = 7 \r\n" );
document.write( "Setting x+2=0 gives x = -2\r\n" );
document.write( "\r\n" );
document.write( "x = 7 and x = -2 are equations of two vertical lines which are the\r\n" );
document.write( "the asymptotes.  You should begin by drawing them in like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since there are asymptotes at -2 and 7, the domain of the function\r\n" );
document.write( "does not include them.  However any other value of x is in the\r\n" );
document.write( "domain, so the domain is \r\n" );
document.write( "\r\n" );
document.write( "(-･, -2) ﾈ (-2, 7) ﾈ (7, ･)\r\n" );
document.write( "\r\n" );
document.write( "Now we can find the horizontal asymptote by using the rules:\r\n" );
document.write( "\r\n" );
document.write( "1. If the degree of the numerator is greater than the degree of the\r\n" );
document.write( "   denominator, then there is no horizontal asymptote.\r\n" );
document.write( "2. If the degree of the numerator is less than the degree of the\r\n" );
document.write( "   numerator, then the horizontal asymptote is the x-axis, whose\r\n" );
document.write( "   equation is y = 0.\r\n" );
document.write( "3. If the degrees of the numerator and the denominato are the same\r\n" );
document.write( "   then the equation of the horizontal asymptote is \r\n" );
document.write( "   y = (leading coeff of numerator)/(leading coeff of denominator)\r\n" );
document.write( "\r\n" );
document.write( "In f(x), we have the 3rd case, so the horizontal asymptote has\r\n" );
document.write( "equation y = 1/1 or y = 1.  \r\n" );
document.write( "\r\n" );
document.write( "So we draw in the horizontal asymptote:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we get a few points, say (-5, 4/9), (-4, 7/22), (-3,0), (-1,1), \r\n" );
document.write( "(1,4/9), (2, 1/4), (3,0), (6,-3 3/8), (8, 5 1/2) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now to find the range.  Oftentimes we have to omit the value of y \r\n" );
document.write( "where there is a horizontal asymptote from the range.  However, this \r\n" );
document.write( "is one of the unusual cases of a graph which crosses its horizontal \r\n" );
document.write( "asymptote y=1 at the point (-1,1). So we cannot rule out any number \r\n" );
document.write( "in the range, and so the range of f(x) is (-･, ･).\r\n" );
document.write( "\r\n" );
document.write( "Hopefully something is here that you were looking for.  If not, post \r\n" );
document.write( "again, giving the instructions as to what you are supposed to do \r\n" );
document.write( "with f(x).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( " \n" ); document.write( "
\n" );