1. ## rational functions

sorry for asking this again, i need to finish this by today so that i can submit this by tom..

Sketch the graph of function Q(x) = x^3 - 1 / x^3 + 1. Determine the prime
factorization of Q(x) and graph the polynomial function.

Thanks !

2. Originally Posted by woooo
sorry for asking this again, i need to finish this by today so that i can submit this by tom..

Sketch the graph of function Q(x) = x^3 - 1 / x^3 + 1. Determine the prime
factorization of Q(x) and graph the polynomial function.

Thanks !
Key features:

$\displaystyle Q(x) = \frac{(x^3 + 1) - 2}{x^3 + 1} = 1 - \frac{2}{x^3 + 1} = -\frac{2}{(x+1)(x^2 - x + 1)} + 1$.

y-intercept: Substitute x = 0 and solve for y.

x-intercept: Substitute y = 0 and solve for x. So solve $\displaystyle x^3 - 1 = 0$.

Vertical asymptote: By inspection, x = -1.

Horizontal asymptote: By inspection, y = 1.

x-coordinates of stationary points: Solve Q'(x) = 0. So solve \frac{6x^2}{(x^3 + 1)^2}[/tex]. Test nature. Now get y-coordinates.

Now draw the shape that fits the above features.

Edit: And please DON'T double post.