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M3-024-A06-V02
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F-IF.7.b
Warmup
M3-024-A06-V02
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Write exact domain and range sets from graph features
Problem
An absolute-value graph has vertex \((3,~4)\) and opens downward. State the exact domain and range, whether each set is continuous or discrete, the bound inclusion, and the vertex evidence.
Answer choices
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A
Domain: all real numbers, continuous with no boundary. Range: (−∞,4], continuous with attained maximum 4. Boundary evidence: downward vertex (3,4).
B
Domain: all real numbers, continuous with no boundary. Range: (−∞,4), continuous with excluded maximum 4. Boundary evidence: vertex output omitted.
C
Domain: (−∞,4], continuous with maximum input 4. Range: all real numbers, continuous with no boundary. Boundary evidence: the two sets are swapped.
D
Domain: all integers, discrete with no finite bound. Range: integers at most 4, discrete with maximum 4. Boundary evidence: isolated outputs.
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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
