document.write( "Question 328155: How would I find the vertical and horizontal asymtotes of the following function?\r
\n" ); document.write( "\n" ); document.write( "g(x)=5x-2/4x^2-4x-3 \n" ); document.write( "

Algebra.Com's Answer #235104 by edjones(8007) $\"\"$ $\"About$

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g(x)=5x-2/4x^2-4x-3
\n" ); document.write( "The denominator cannot equal zero so the vertical asymptotes when one of the zeros of occurs.
\n" ); document.write( "4x^2-4x-3=0
\n" ); document.write( "4*-3=-12, the 2 factors of -12 whose sum is -4 is -6 and +2.
\n" ); document.write( "4x^2+2x-6x-3=0
\n" ); document.write( "2x(2x+1)-3(2x+1)=0
\n" ); document.write( "(2x-3)(2x+1)=0
\n" ); document.write( "2x=3, x=3/2
\n" ); document.write( "2x=-1, x=-1/2
\n" ); document.write( "x=3/2 and x=-1/2 the vertical asymptotes.
\n" ); document.write( "If the largest exponent in the numerator is smaller than the largest in the denominator the the horizontal asymptote is zero. Graphs frequently cross horizontal asymptotes as in this case.
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\n" ); document.write( " $\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C%285x-2%29%2F%284x%5E2-4x-3%29%29\"$ \n" ); document.write( "

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