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# FP1: Asymptotes watch

1. Click ^ above to see question.

How do you know for certain y = 0 is an asymptote, it says so in the mark scheme? What method do you use to test that theory.
2. (Original post by Konnichiwa)

Click ^ above to see question.

How do you know for certain y = 0 is an asymptote, it says so in the mark scheme? What method do you use to test that theory.
You find horizontal asymptotes by looking at the function's behaviour as . Easiest way would be to expand out the brackets and multiply the top and bottom by and then see what happens as
3. (Original post by Konnichiwa)

Click ^ above to see question.

How do you know for certain y = 0 is an asymptote, it says so in the mark scheme? What method do you use to test that theory.
As above:
As x tends to infinity, the denominator tends to infinty. Despite this, like the curve it will never quite reach the x-axis, despite coming infinitesimally close.
4. If you use that method on enough, you will be able to see that rational functions always follow these rules:

If the numerator is a higher degree than the denominator, then there is no horizontal asymptote (but an oblique one).

If the numerator is the same degree as the denominator, then there is a horizontal asymptote at y equals the numerator's leading coefficient divided by the denominator's leading coefficient.

If the numerator is a lower degree than the denominator, then the horizontal asymptote is at y=0.
5. (Original post by aznkid66)
If the numerator is one degree higher than the denominator, then there is no horizontal asymptote (but an oblique one).
Fixed that for you.
6. (Original post by Mr M)
Fixed that for you.

But wait, if you have f(x)/g(x), and f(x) is a higher degree than g(x), then there will be no horizontal asymptote because f(x) divided by g(x) without the remainder will not be a constant function but a polynomial with a degree greater than or equal to 1.

So you should've edited the oblique part instead ^^
7. (Original post by aznkid66)

But wait, if you have f(x)/g(x), and f(x) is a higher degree than g(x), then there will be no horizontal asymptote because f(x) divided by g(x) without the remainder will not be a constant function but a polynomial with a degree greater than or equal to 1.

So you should've edited the oblique part instead ^^
Nope, I wanted to leave the reference to oblique asymptotes there as TSR users will encounter them.

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