#18 02.06 Rational Functions and Asymptotes

Mathematics
Tutor: None Selected Time limit: 1 Day

May 13th, 2015

The domain is all real numbers except -1.

There is a vertical asymptote x=-1 (f(x) -> -∞ as x->-1-0 and f(x)->+∞ as x->-1+0).

And no horizontal asymptotes (f(x) = [2x - 2x/(x+1)] ->∞ as x->∞).

Also, as x->+-∞, f(x)/x = 2x/(x+1) -> 2 and
f(x)-2x = 2x*[1/(x+1) - 1] = -2x/(x+1) -> -2.
So f(x) has an obique (slanted) asymptote y=2x-2.

May 13th, 2015

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May 13th, 2015
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