Math
posted by Dave .
How do you find the vertical and horizontal assymptotes of the graph of the rational function?
f(x)= 3x^25x+2/6x^25x+1
f(x)= 2x+3/(ãx^22x+3)

Vertical asymptotes in rational functions usually come from the denominator approaching zero.
In
f(x)= (3x^25x+2)/(6x^25x+1)
the denominator can be factorized as:
(3x1)(2x1)
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 ±∞.