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M3-021-A06-V03
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F-IF.4
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M3-021-A06-V03
Interpret key features of rational, square-root, cube-root, and other function models in context.
Determine root-model domain, range, anchor, and monotonicity
Problem
Analyze \(y~=~\sqrt[3]{x~-~4}~-~2\). Identify the root family and radicand condition, state the domain and range, locate the anchor, and give the intervals of increase and decrease.
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A
Root: square root with x−4≥0. Domain: [4,∞). Range: [−2,∞). Anchor: left endpoint (4,−2). Monotonicity: increasing on [4,∞); decreasing nowhere.
B
Root: cube root with x−4≥0. Domain: [4,∞). Range: [−2,∞). Anchor: left endpoint (4,−2). Monotonicity: increasing on [4,∞); decreasing nowhere.
C
Root: cube root with unrestricted radicand. Domain: (−∞,∞). Range: (−∞,∞). Anchor: central point (−4,−2). Monotonicity: decreasing on all real numbers; increasing nowhere.
D
Root: cube root with unrestricted radicand. Domain: (−∞,∞). Range: (−∞,∞). Anchor: central point (4,−2). Monotonicity: increasing on all real numbers; decreasing nowhere.
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Curriculum context
Standard F-IF.4
Category Functions
Domain Interpreting Functions
Objective Interpret key features of rational, square-root, cube-root, and other function models in context.
Problem type Determine root-model domain, range, anchor, and monotonicity
