Problem

A square-root graph has endpoint \((2,~-1)\) and extends right and upward. State the exact domain and range, whether each set is continuous or discrete, the bound inclusion, and the boundary evidence.

Square-root graph beginning at 2 comma negative 1 and extending right and upward.

Big Picture

What this problem is really about

For a square-root graph, the endpoint controls both interval descriptions. Project that solid endpoint to each axis to read the included lower boundary, then follow the curve’s arrow to determine which direction each interval continues. Writing the inequalities and interval notation side by side helps keep the brackets and infinities consistent.

Answer choices

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Domain: [2,∞), continuous with included lower bound 2. Range: [−1,∞), continuous with included lower bound −1. Boundary evidence: endpoint (2,−1).

Domain: 2,3,4,..., discrete with first input 2. Range: −1,0,1,..., discrete with first output −1. Boundary evidence: isolated plotted points.

Domain: [−1,∞), continuous with included lower bound −1. Range: [2,∞), continuous with included lower bound 2. Boundary evidence: the endpoint sets swapped bounds.

Domain: (2,∞), continuous with excluded lower bound 2. Range: (−1,∞), continuous with excluded lower bound −1. Boundary evidence: endpoint omitted.

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A square-root graph has endpoint \((2,~-1)\) and extends right and upward. State the exact domain and range, whether each set is continuous or discrete, the bound inclusion, and the boundary evidence.

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