Thread: 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

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


Therefore the equation of the function is:



But of course you can choose



Then the function is