College Algebra, Chapter 4, 4.2, Section 4.2, Problem 18

Sketch the graph of polynomial function $P(x) = (2x-1)(x+1)(x+3)$ make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree of 3 and a positive leading coefficient. Thus, its end behaviour is $y \rightarrow \infty \text{ as } x \rightarrow \infty \text{ and } y \rightarrow -\infty \text{ as } x \rightarrow \infty$. To solve for the $y$-intercept, we set $x = 0$

$
\begin{equation}
\begin{aligned}
y &= (2(0)-1)(0+1)(0+3)\\
\\
y &= (-1)(1)(3) = -3
\end{aligned}
\end{equation}
$

To determine the $x$-intercept, we set $y = 0$. In this case, we have
$\displaystyle x = \frac{1}{2}, -1$ and $-3$.