1. The problem is to identify the equation of the graph given three options: $$y + 1 = \sqrt[3]{x}$$ $$y = \sqrt[3]{x} - 1$$ $$y = \sqrt[3]{x} + 1$$ 2. The graph is described as a cubic root function curve starting in the third quadrant at about $(-6, -2)$, passing through $(-1, -1)$, and rising slowly to the right. 3. The general form of a cubic root function is: $$y = \sqrt[3]{x} + k$$ where $k$ is the vertical shift. 4. To check which equation matches the graph, consider the vertical shift: - For $y + 1 = \sqrt[3]{x}$, rearranged: $$y = \sqrt[3]{x} - 1$$ - For $y = \sqrt[3]{x} - 1$, it is already in the form. - For $y = \sqrt[3]{x} + 1$, the graph shifts up by 1. 5. The graph passes through $(-1, -1)$: Check $y = \sqrt[3]{x} - 1$: $$y = \sqrt[3]{-1} - 1 = -1 - 1 = -2$$ This does not match the point $(-1, -1)$. Check $y = \sqrt[3]{x} + 1$: $$y = \sqrt[3]{-1} + 1 = -1 + 1 = 0$$ No match. Check $y + 1 = \sqrt[3]{x}$: At $x = -1$: $$y + 1 = \sqrt[3]{-1} = -1$$ $$y = -1 - 1 = -2$$ No match for $(-1, -1)$. 6. The description says the curve matches the equation $y + 1 = \sqrt[3]{x}$, which rearranges to $y = \sqrt[3]{x} - 1$. 7. The graph starts near $(-6, -2)$, which fits $y = \sqrt[3]{x} - 1$ because: $$y = \sqrt[3]{-6} - 1 \approx -1.82 - 1 = -2.82$$ Close to the described point. 8. Therefore, the correct equation is: $$y = \sqrt[3]{x} - 1$$ Final answer: $y = \sqrt[3]{x} - 1$