## Precalculus (6th Edition) Blitzer

$3$
From the graph, the function is increasing as the value of $x$ is increasing, other than at the point $x=0$. At $x=0$ the slope of the graph is zero, and that point is known as the point of inflection. So, the number of turning points is $2$. \begin{align} & \text{Smallest}\ \text{degree}\ \text{of}\ \text{polynomial}=\left( \text{Number}\ \text{of}\ \text{turning}\ \text{point} \right)\text{+1} \\ & =2+1 \\ & =3 \end{align} Hence, the smallest degree of the polynomial is $3$.