1. The problem asks us to analyze the behavior of the graphs of the functions $f(x) = x^3 - 1$ and $g(x) = -x^3 + 1$ for large values of $x$. 2. The key idea is to understand the end behavior of cubic functions. For large positive or negative $x$, the highest degree term dominates the function's value. 3. For $f(x) = x^3 - 1$, as $x \to +\infty$, $x^3$ grows very large positively, so $f(x) \to +\infty$. As $x \to -\infty$, $x^3$ becomes very large negatively, so $f(x) \to -\infty$. 4. For $g(x) = -x^3 + 1$, as $x \to +\infty$, $-x^3$ becomes very large negatively, so $g(x) \to -\infty$. As $x \to -\infty$, $-x^3$ becomes very large positively, so $g(x) \to +\infty$. 5. In summary, $f(x)$ increases without bound for large positive $x$ and decreases without bound for large negative $x$. Conversely, $g(x)$ decreases without bound for large positive $x$ and increases without bound for large negative $x$. 6. This means the graphs of $f$ and $g$ are reflections of each other about the horizontal axis and vertical axis combined, showing opposite end behaviors. Final answer: For large $x$, $f(x) \to +\infty$ as $x \to +\infty$ and $f(x) \to -\infty$ as $x \to -\infty$; $g(x) \to -\infty$ as $x \to +\infty$ and $g(x) \to +\infty$ as $x \to -\infty$.