# Thread: How do I write an equation with a slant asymptote?

1. ## How do I write an equation with a slant asymptote?

Hi everyone,

We recently learned in math class that to get the equation of a slant asymptote of an equation, divide the numerator by the denominator. I'm understanding how to divide polynomials, but now I get a freeform homework question that says write an equation of a function with a slant asymptote of y = x ! How do I do this? I'm used to going the other way!

Thanks

2. Originally Posted by gobbajeezalus
Hi everyone,

We recently learned in math class that to get the equation of a slant asymptote of an equation, divide the numerator by the denominator. I'm understanding how to divide polynomials, but now I get a freeform homework question that says write an equation of a function with a slant asymptote of y = x ! How do I do this? I'm used to going the other way!

Thanks
If you divide the numerator by the dnominator then you get the term of the asymptote and a remainder which is approaching zero if x approaches infinity. You now have to choose such a remainder. The most simple case is that
$r = \dfrac1x$

Therefore the equation of the function is:

$y = x + \dfrac1x = \dfrac{x^2+1}x$

But of course you can choose

$r = \dfrac{2x+3}{x^3+x^2}$

Then the function is

$y = x+ \dfrac{2x+3}{x^3+x^2} = \dfrac{x^4+x^3+2x+3}{x^3+x^2}$