1. Stated Problem: Find the intersection points of the function $F(x) = x^3 - 1$ with the line $y + 7 = 0$. 2. Rewrite the line equation to standard form: $y + 7 = 0 \implies y = -7$. 3. Since $F(x) = y$, set the function equal to the line: $$x^3 - 1 = -7$$ 4. Simplify the equation: $$x^3 - 1 + 7 = 0 \implies x^3 + 6 = 0$$ 5. Solve for $x$: $$x^3 = -6 \implies x = \sqrt[3]{-6} = -\sqrt[3]{6}$$ 6. Calculate numerical approximation: $$x \approx -1.817$$ 7. The $y$-coordinate at the intersection is $y = -7$. 8. Final Answer: The function $F(x) = x^3 - 1$ intersects the line $y = -7$ at the point $$\left(-\sqrt[3]{6}, -7\right) \approx (-1.817, -7)$$.