1. **State the problem:** Identify the equation of the graph described. 2. **Analyze the given options:** - Option 1: $y + 1 = \sqrt[3]{x}$ - Option 2: $y - 1 = \sqrt[3]{x}$ - Option 3: $y = \sqrt[3]{x - 1}$ 3. **Recall the cube root function properties:** - The basic cube root function is $y = \sqrt[3]{x}$, which passes through the origin $(0,0)$. - Shifting the graph vertically by $k$ units changes the equation to $y = \sqrt[3]{x} + k$. - Shifting horizontally by $h$ units changes the equation to $y = \sqrt[3]{x - h}$. 4. **Check the graph points:** - The graph passes through $(-1, 0)$ and $(0, 1)$. 5. **Test Option 2: $y - 1 = \sqrt[3]{x}$** - Rearranged: $y = \sqrt[3]{x} + 1$ - At $x = -1$, $y = \sqrt[3]{-1} + 1 = -1 + 1 = 0$ (matches the point $(-1,0)$). - At $x = 0$, $y = \sqrt[3]{0} + 1 = 0 + 1 = 1$ (matches the point $(0,1)$). 6. **Test Option 1: $y + 1 = \sqrt[3]{x}$** - Rearranged: $y = \sqrt[3]{x} - 1$ - At $x = -1$, $y = -1 - 1 = -2$ (does not match $(-1,0)$). 7. **Test Option 3: $y = \sqrt[3]{x - 1}$** - At $x = -1$, $y = \sqrt[3]{-1 - 1} = \sqrt[3]{-2} \approx -1.26$ (does not match $0$). 8. **Conclusion:** The graph matches the equation $y - 1 = \sqrt[3]{x}$. **Final answer:** $$y - 1 = \sqrt[3]{x}$$