General functions practice
Find the domain and range, then graph eight transformed square-root and cube-root functions on unit grids. Choose square roots, cube roots or balanced mixed practice with separate completed graph keys.
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Find the domain and range. Plot the endpoint or center and useful exact points, then draw the radical curve with arrows where it continues.
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Each worksheet contains eight direct radical functions. Mixed practice gives four square roots and four cube roots; focused modes retain positive and negative coefficients, shifts and nonunit stretches.
For y = a root_n(x - h) + k, use t as the root value: x = h + t^n and y = k + at. Square roots use t >= 0 and begin at the included endpoint (h, k). Cube roots use every real t and pass through the center (h, k).
The separate key states the global domain and range, marks exact on-grid points and draws only the visible part of the continuing curve. Grid boundaries never become fake domain endpoints.
Learning objective
Use an endpoint or center and exact transformed points to graph square-root and cube-root functions with their global domains and ranges.
Worked example
Endpoint (1, 3); domain x >= 1; range y <= 3. Useful points include (2, 1) and (5, -1).
The radicand starts at zero when x = 1. The negative coefficient reflects the parent square-root graph downward, and its magnitude doubles each vertical change.
Teaching notes
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Choose square roots, cube roots or balanced mixed practice. Each sheet has eight distinct transformed functions, global domain and range prompts, and four graphs per page.
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