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M3-024-A06-V04
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F-IF.7.b
Warmup
M3-024-A06-V04
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Write exact domain and range sets from graph features
Problem
A cube-root graph is centered at \((1,~-2)\). State the exact domain and range, classify their continuity and boundaries, and explain why the center is not an endpoint.
Answer choices
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A
Domain: all real numbers, continuous with no boundary. Range: [−2,∞), continuous with included lower bound −2. Boundary evidence: only outputs above the center are kept.
B
Domain: [1,∞), continuous with included lower bound 1. Range: [−2,∞), continuous with included lower bound −2. Boundary evidence: the center is treated as an endpoint.
C
Domain: (−∞,1], continuous with included upper bound 1. Range: (−∞,−2], continuous with included upper bound −2. Boundary evidence: the center is treated as a terminal point.
D
Domain: all real numbers, continuous with no boundary. Range: all real numbers, continuous with no boundary. Boundary evidence: translating a cube-root graph creates no endpoint.
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Curriculum context
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 Write exact domain and range sets from graph features
