How do you find all the asymptotes for function #y = x/(x-6) #?
1 Answer
Explanation:
3 types of asymptotes : Vertical, horizontal and oblique.
Vertical :
The straight line
Let
The domain of f(x) is
We generally find a vertical asymptote in a rational function, when the value of denominator is equal to 0 (except if numerator is zero in the same time)
Look at
We comply with the starting conditions :
Horizontal :
The straight line
To find easily the limit when x go to
Limit calculation :
And
Then :
Do the same reasoning when
Therefore :
Oblique :
No oblique asymptote because
To sum up, look at the graph below :
Note :