To find the product function $(f \cdot g)(x)$ for the polynomial functions $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$, substitute the expressions into the multiplication formula: $(f \cdot g)(x) = (x + 2)(x^2 - 3x - 4)$. Multiply the polynomials by distributing: $x(x^2 - 3x - 4) + 2(x^2 - 3x - 4)$. This expands to $x^3 - 3x^2 - 4x + 2x^2 - 6x - 8$. Combining the like terms yields the final product function: $(f \cdot g)(x) = x^3 - x^2 - 10x - 8$.