posted by Dave .
How do you find the vertical and horizontal assymptotes of the graph of the rational function?
Vertical asymptotes in rational functions usually come from the denominator approaching zero.
the denominator can be factorized as:
at x=1/3 or x=1/2, the denominator becomes zero, and hence a vertical asymptote. You also need to check if the numerator vanishes at the same points, in which case the point will be undefined.
To find the horizontal asymptotes, do a long division, and the resulting leading constant (1/2) is the horizontal asymptote. Take care to determine from which side of y=1/2 the curve approaches the asymptote as x approaches ±∞.