1. **Problem Statement:** We need to determine which cubic equation matches the graph described. 2. **Given Information:** The graph is a cubic function with roots near $x = -4$, $x = 6$, and $x = 1$. The curve starts low on the left, peaks near $x = -3$, dips near $x = 3$, and rises sharply to the right. 3. **Possible Equations:** - $f(x) = (x + 4)(x - 6)(x - 1)$ - $f(x) = (x + 4)(x + 6)(x - 1)$ - $f(x) = (x + 4)(x + 6)(x + 1)$ - $f(x) = (x - 4)(x + 6)(x + 1)$ 4. **Step: Analyze roots:** The graph crosses the x-axis near $-4$, $6$, and $1$. So the roots must be exactly these values. 5. **Check each equation's roots:** - $(x + 4)(x - 6)(x - 1)$ has roots at $x = -4, 6, 1$ (matches exactly). - $(x + 4)(x + 6)(x - 1)$ has roots at $x = -4, -6, 1$ (does not match). - $(x + 4)(x + 6)(x + 1)$ has roots at $x = -4, -6, -1$ (does not match). - $(x - 4)(x + 6)(x + 1)$ has roots at $x = 4, -6, -1$ (does not match). 6. **Step: Confirm behavior:** The graph's shape (peak near $-3$, trough near $3$) is consistent with the cubic having roots at $-4, 1, 6$ and the leading coefficient positive (since it rises to the right). 7. **Conclusion:** The equation $f(x) = (x + 4)(x - 6)(x - 1)$ best represents the graph. **Final answer:** $$f(x) = (x + 4)(x - 6)(x - 1)$$