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M3-024-A06-V03
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F-IF.7.b
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M3-024-A06-V03
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Write exact domain and range sets from graph features
Problem
A step graph covers every input on \([0,~10]\) and has only outputs \(5\), \(8\), and \(12\). State the exact domain and range, classify each as continuous or discrete, and cite the boundary evidence.
Answer choices
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A
Domain: 0,3,7,10, finite discrete set. Range: 5,8,12, finite discrete set. Boundary evidence: only transition inputs are counted.
B
Domain: [0,10], continuous interval with included endpoints. Range: [5,12], continuous interval. Boundary evidence: every output between 5 and 12 is assumed.
C
Domain: 5,8,12, finite discrete set. Range: [0,10], continuous interval with included endpoints. Boundary evidence: the input and output sets are swapped.
D
Domain: [0,10], continuous interval with included endpoints. Range: 5,8,12, finite discrete set. Boundary evidence: closed steps cover every input from 0 through 10.
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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
