f(x)=(x2−2ax)/(x−a) where a is positive. The question asks to give equations for the 2 asymptotes. The first is obvious: x=a. The other asymptote is y=x−a but I am unsure how to derive this.

imire37 2022-08-13 Answered
Asymptotes for a function
f ( x ) = x 2 2 a x x a
where a is positive.
The question asks to give equations for the 2 asymptotes. The first is obvious: x=a. The other asymptote is y=x−a but I am unsure how to derive this.
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Answers (1)

Dominic Paul
Answered 2022-08-14 Author has 17 answers
Rewrite the function:
f ( x ) = x 2 2 a x x a = x 2 2 a x + a 2 a 2 x a = ( x a ) 2 a 2 x a = x a a 2 x a
Now both the stated asymptotes are obvious: a vertical one (x=a) and an oblique one (y=x−a).
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