# Thread: need help creating a rational function (no clue where to start)

1. ## need help creating a rational function (no clue where to start)

lim f(x) = 2 x -> infinty
lim f(x) = -2 x-> - infinty
lim f(x) = - infinty x-> -4
lim f(x) = - infinty x-> 2-
lim f(x) = infinty x-> 2+

relative min of 0 at x=2
relative max of -0.900466 at x=0.442818
concave down (-infinty, -4) (-4,-2) (6.835351, infinty)
concave up (2,6.835351)
x-inter (4,0)
y-inter (0,-1)
vertical asymptotes at x=2, x=4

2. The fact that "lim f(x) = - infinty as x-> -4" and "lim f(x) = - infinty as x-> 2-" tells you that there must be factors of (x+ 4) and (x- 2) in the denominator. Further, since the limit, as x goes to 4 from "both sides" is $-\infty$ there must be a factor of $(x+ 4)^2$ in the denominator. That means that the degree of the denominator is at least 3. In order that the limits as x goes to $+\infty$ and $-\infty$ be non-zero real numbers, the degree of the numerator and denominator must be the same. I suggest you write the function as
$\frac{ax^3+ bx^2+ cx+ d}{(x- 2)(x+4)^2}$
and try to determine values for a, b, c, and d that make the other requirements true.

3. Thanks so much is there a method to coming up with those numbers or is it just plug and chug