# How do you find the end behavior of  f(x) = (x-1)(x+2)(x+3)?

See explanation

#### Explanation:

Expanding it gives us

$f \left(x\right) = {x}^{3} + 4 {x}^{2} + x - 6 \implies f \left(x\right) = {x}^{3} \cdot \left(1 + \frac{4}{x} + \frac{1}{x} ^ 2 - \frac{6}{x} ^ 3\right)$

Hence $f \left(x\right) \to + \infty$ when $x \to + \infty$

and $f \left(x\right) \to - \infty$ when $x \to - \infty$