Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.
Transform a fixed set of square-root parent points
Problem
For \(y=\sqrt{x}\), evaluate the parent inputs \(u=0,1,4,9\) and record each point \((u,\sqrt{u})\). Use the first point and the square-root restrictions to state the endpoint, domain, and range, then identify the point-and-feature set supported by your calculations.
Square-root graphs are easiest to anchor with inputs whose roots are exact. We’ll evaluate a fixed set of nonnegative perfect-square inputs, preserve input-output order in the plotted points, and use the included endpoint and principal-root restriction to determine the graph’s domain and range.
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