Question

Create a (simplified) rational function that has the following asymptotes.(show work) y=0, x=-3, x=0, and x=2

Answer 1

Hmmmm. f(x)= e^-x * 1/[(x+3)(x)(x-2)]

Answer 2

I think rational functions are ratios of polynomials, so forget the e^-x and just use

1/[(x+3)(x)(x-2)]

or, the numerator could be any polynomial of degree less than 3. It will still approach y=0 as x gets large.