1. The problem is to find the domain and range of the function $$F(x) = x^3 - 1$$. 2. The domain of a function is the set of all possible input values $x$ for which the function is defined. Since $x^3$ is defined for all real numbers and subtracting 1 does not restrict the domain, the domain is all real numbers. 3. The range is the set of all output values $F(x)$. Since $x^3$ is a cubic function, it can produce all real values from $-\infty$ to $\infty$. 4. Subtracting 1 shifts the entire graph down by 1 unit, but does not change the infinite extent of the values. Therefore, the range is also all real numbers. 5. In summary: - Domain: $$(-\infty, \infty)$$ - Range: $$(-\infty, \infty)$$