Quick check on asymptotes

[fred2028]

So after reading purplemath.com's lessons about finding asymptotes from equations of rational functions, here's what I've learned. Please correct any mistakes and state any exceptions ... If any.

If the degree of the polynomial in the numerator is greater than that in the denominator, then there is a slanted asymptote at y=the quotient of the 2 polynomials.

If the degree of the polynomial in the denominator is greater than that of the numerator, the asymptote is at y=0, or x-axis.

If both degrees are the same, then the asymptote is at y=(numerator leading coefficient) / (denominator leading coefficient).

Thanks a lot!

 

[tkhunny]

So CLOSE!!

Let's fix and expand this one:

If the degree of the polynomial in the numerator is greater than that in the denominator, then there is a slanted asymptote at y=the quotient of the 2 polynomials.

It must be broken into two:

1) If the degree of the polynomial in the numerator is ONE greater than that in the denominator, then there is a slanted asymptote at y=the quotient of the 2 polynomials WITHOUT THE REMAINDER.

2) If the degree of the polynomial in the numerator is MORE THAN ONE greater than that in the denominator, then there is a HIGHER PLANE CURVE asymptote at y=the quotient of the 2 polynomials WITHOUT THE REMAINDER.

Those "Higher Plan Curves" are parabolas, cubics, and stuff like that.

 

[fred2028]

Oh OK. So that's how curved asymptotes are formed. Thanks!