Problem preview

F-IF.7.b Warmup M2-022-A02-V02

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 cube-root parent points

Problem

For \(y=\sqrt[3]{x-2}+3\), let \(u=x-2\) and transform each parent point \((u,\sqrt[3]{u})\) using \((u,\sqrt[3]{u})\to~(u+2,\sqrt[3]{u}+3)\) for \(u=-8,-1,0,1,8\). Record all five points and identify the transformed center.

Source graph of the cube-root parent points (−8,−2), (−1,−1), (0,0), (1,1), and (8,2), corresponding to u=−8,−1,0,1,8.

Answer choices

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Points (−10,1), (−3,2), (−2,3), (−1,4), (6,5); center (−2,3).

Points (−6,−5), (1,−4), (2,−3), (3,−2), (10,−1); center (2,−3).

Points (−5,0), (2,1), (3,2), (4,3), (11,4); center (3,2).

Points (−6,1), (1,2), (2,3), (3,4), (10,5); center (2,3).

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Curriculum context

Course: Math II
Standard: F-IF.7.b
Category: Functions
Domain: Interpreting Functions
Objective: Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type: Transform a fixed set of cube-root parent points