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 !
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.