document.write( "Question 1196010: Write an equation for a rational function with the given characteristics.
\n" ); document.write( "Vertical asymptotes at x = −4 and x = 8, x-intercepts at (−2, 0) and (1, 0),horizontal asymptote at y = −2 \n" ); document.write( "

Algebra.Com's Answer #828675 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Write an $\"highlight%28cross%28equation%29%29\"$ expression for a rational function with the given characteristics.
\n" ); document.write( "Vertical asymptotes at x = −4 and x = 8, x-intercepts at (−2, 0) and (1, 0),
\n" ); document.write( "horizontal asymptote at y = −2
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "A rational function R(x) is the ratio R(x) =   of two polynomials P(x) and Q(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We want the denominator Q(x) would have the zeroes at x= -4 and x= 8, giving \r\n" );
document.write( "vertical asymptotes.\r\n" );
document.write( "\r\n" );
document.write( "So we take Q(x) as a quadratic function Q(x) = (x-(-4))*(x-8) = (x+4)*(x-8).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we want the numerator P(x) would be zero at x= -2 and x= 1, providing \r\n" );
document.write( "assigned x-intersectios.  So we take the numersator P(x) as a quadratic function\r\n" );
document.write( "\r\n" );
document.write( "    P(x) = a*(x-(-2))*(x-1) = a*(x+2)*(x-1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the ratio    will have the assigned x-intersections and \r\n" );
document.write( "assigned vertical asymptotes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To have the given horizontal asymptote y= 2 at x -- +/- ,  we take a = -2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, finally our rational function is  R(x) = .    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You can re-write the answer in any other equivalent form, if you want or if you need.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );