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Separate polynomial parts from vanishing remainders

By carrying out long division to simplify the rational function (if applicable), find the equation(s) of the horizontal asymptote(s) or oblique asymptote(s) for the following curves.

(a) y=1/(3−x)y=1/(3-x).

(b) y=(2x+1)/(x−2)y=(2x+1)/(x-2).

(c) y=x2/(x−1)y=x^2/(x-1).

(d) y=(x2+2x−3)/(x+2)y=(x^2+2x-3)/(x+2).

CJC · Lecture · Self-Practice 3

Use limits to justify asymptotes; use long division when the rational expression is improper.

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