Compare and discuss the long-run behaviors of the functions below. In each blank, enter either the constant or the polynomial that the rational function behaves like as $x \to \pm \infty$:

$\displaystyle f(x) = \frac{x^3 + 3}{x^3 - 8}$ , $\displaystyle g(x) = \frac{x^2 + 3}{x^3 - 8}$ , and $\displaystyle h(x) = \frac{x^4 + 3}{x^3 - 8}$

$f(x)$ will behave like the function $y =$ as $x \to \pm \infty$. help (formulas)

$g(x)$ will behave like the function $y =$ as $x \to \pm \infty$. help (formulas)

$h(x)$ will behave like the function $y =$ as $x \to \pm \infty$. help (formulas)