Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Analyze a transformed radical graph with anchor, domain, and range
Problem
Analyze \(y~=~\sqrt{x~-~3}~+~2\) relative to \(y~=~\sqrt{x}\). State the transformations, endpoint, domain, and range.
Compare the parent endpoint to the shifted endpoint, then read where the new graph begins.Open full size
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What this problem is really about
A square-root graph is organized around its endpoint, so move that anchor before describing the rest of the curve. The inside shift sets where allowed inputs begin, and the outside shift sets the corresponding output boundary. Once the endpoint is mapped, the graph’s direction tells whether the domain and range extend upward, downward, left, or right.
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