Subjects algebra

Cube Root Shift 04Cac9

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1. The problem is to identify the graph of the equation $$y=\sqrt[3]{x}+2$$. 2. The cube root function $$y=\sqrt[3]{x}$$ is an odd function with a characteristic S-shaped curve passing through the origin (0,0). 3. The equation $$y=\sqrt[3]{x}+2$$ represents a vertical shift of the cube root graph upwards by 2 units. 4. The original cube root graph passes through points like (-8,-2), (0,0), and (8,2). 5. After shifting up by 2, these points become (-8,0), (0,2), and (8,4). 6. Checking the given graph descriptions: - Bottom-left: curve from (-4,-2) to (2,4) - Center: curve from (-2,-4) to (6,2) - Bottom-right: curve from (-6,-4) to (2,2) 7. The shifted cube root graph should pass near (0,2) and rise to (8,4), which matches the bottom-left graph description best. 8. Therefore, the graph corresponding to $$y=\sqrt[3]{x}+2$$ is the bottom-left graph. Final answer: Bottom-left graph.