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.
Write a square-root equation from an endpoint, direction, and scale
Problem
Write the square-root equation for the graph with endpoint \((3,2)\), increasing to the right at parent scale. Start with \(y=a\sqrt{x-h}+k\), determine \(a\), \(h\), and \(k\) from the features, and verify the graph's value \(\text{one}~\text{unit}\) to the right of the endpoint.
A square-root equation can be reconstructed from its endpoint, direction, and scale. We’ll place the endpoint into transformed-root form, use the branch direction to fix the sign of the scale, and test a convenient input one unit from the endpoint.
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