Problem

Derive the exact graph fingerprint for \(y=-\sqrt[3]{x+1}\). Identify the horizontal translation and reflection, locate the center, determine direction, domain, and range, and verify the fingerprint by evaluating \(x=-2\) and \(x=0\).

Answer choices

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Cube-root graph shifted left 1 without reflection; center (−1,0); increasing; all-real domain and range; points (−2,−1), (0,1).

Cube-root graph shifted left 1 and up 1, then reflected; center (−1,1); decreasing; all-real domain and range; points (−2,2), (0,0).

Cube-root graph shifted right 1 and reflected across the x-axis; center (1,0); decreasing; all-real domain and range; points (0,1), (2,−1).

Cube-root graph shifted left 1 and reflected across the x-axis; center (−1,0); decreasing; all-real domain and range; points (−2,1), (0,−1).

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