Chapter 5 - Exponential and Logarithmic Functions - 5.9 Building Exponential, Logarithmic, and Logistic Models from Data - 5.9 Assess Your Understanding - Page 342: 13

Answer may vary. $f(x)=\frac{1}{3}(x+3)(x+1)^2(x-2)$

Answer may vary. Step 1. Identify zeros $x=-3,2$ and $x=-1$ (multiplicity 2), write the function as $f(x)=a(x+3)(x+1)^2(x-2)$ Step 2. Use point $(0,-2)$, we have $f(0)=-6a=-2$ and $a=\frac{1}{3}$ Step 3. Thus we have $f(x)=\frac{1}{3}(x+3)(x+1)^2(x-2)$