Problem

For \(y~=~\sqrt{x~-~2}~+~1\), state \(a\), \(h\), and \(k\); give the endpoint, domain, and range; and map the parent square-root anchors with inputs \(1\), \(4\), and \(9\).

Parent square-root graph with standard anchor dots on a coordinate grid.

Big Picture

What this problem is really about

Start from the square-root parent's endpoint and perfect-square anchors, then apply the same horizontal and vertical translation to every point. The radicand boundary fixes the transformed endpoint and domain, while the outside shift and scale determine the output direction and range. Exact radicands keep the mapped anchor coordinates easy to audit.

Answer choices

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Preview only

Parameters: a=1, h=2, k=−1. Endpoint: (2,−1). Domain: [2,∞). Range: [−1,∞). Anchors: (3,0), (6,1), (11,2).

Parameters: a=1, h=2, k=1. Endpoint: (2,1). Domain: [2,∞). Range: [1,∞). Anchors: (3,2), (6,3), (11,4).

Parameters: a=−1, h=2, k=1. Endpoint: (2,1). Domain: [2,∞). Range: (−∞,1]. Anchors: (3,0), (6,−1), (11,−2).

Parameters: a=1, h=−2, k=1. Endpoint: (−2,1). Domain: [−2,∞). Range: [1,∞). Anchors: (−1,2), (2,3), (7,4).

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For \(y~=~\sqrt{x~-~2}~+~1\), state \(a\), \(h\), and \(k\); give the endpoint, domain, and range; and map the parent square-root anchors with inputs \(1\), \(4\), and \(9\).

What this problem is really about

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