Chapter 3 - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 266: 46

$x \rightarrow\infty$ $P(x)\rightarrow -\infty$ $x\rightarrow\ - \infty$ $P(x)\rightarrow \infty$

$P(x) = -\frac{1}{8}x^{3}+\frac{1}{4}x^{2}+12x$ $Q(x)=-\frac{1}{8}x^{3}$ $x \rightarrow\infty$ $-\frac{1}{8} x^{3} \rightarrow-\frac{1}{8}(\infty)(\infty)(\infty) = - \infty$ $P(x)\rightarrow -\infty$ $x\rightarrow\ - \infty$ $-\frac{1}{8}x^ {3}\rightarrow-\frac{1}{8}(-\infty)(-\infty)(-\infty) = \infty$ $P(x)\rightarrow \infty$