1. **State the problem:** We need to identify which graph corresponds to the function $$g(x) = (x + 1)(x - 2)(x + 5)$$. 2. **Recall the roots:** The roots of the polynomial are the values of $x$ that make $g(x) = 0$. From the factors, the roots are: $$x = -1, \quad x = 2, \quad x = -5$$ 3. **Analyze the behavior:** Since $g(x)$ is a cubic polynomial with leading term $x^3$ (positive leading coefficient), as $x \to \infty$, $g(x) \to \infty$, and as $x \to -\infty$, $g(x) \to -\infty$. 4. **Check the graphs:** - **Graph A:** Has roots near $-5$, $-1$, and $2$, matching the roots of $g(x)$. It starts from bottom-left (negative $y$ as $x \to -\infty$), crosses the x-axis at these roots, and ends going upward in the top-right quadrant (positive $y$ as $x \to \infty$). - **Graph B:** Does not have roots matching the polynomial factors and starts from top-left going downward, which contradicts the end behavior of $g(x)$. 5. **Conclusion:** Graph A matches the roots and end behavior of $g(x)$. **Final answer:** Graph A corresponds to $$g(x) = (x + 1)(x - 2)(x + 5)$$.