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M3-021-A07-V02
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F-IF.4
Warmup
M3-021-A07-V02
Interpret key features of rational, square-root, cube-root, and other function models in context.
Label monotonicity on every connected domain interval
Problem
For \(y~=~-\sqrt{x}~+~4\), state the domain, list every connected interval of increase and decrease, explicitly identify any empty category, and explain the boundary notation at \(x~=~0\).
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A
Domain: (0,∞). Connected rows: decreasing on (0,∞). Empty category: no increasing interval. Boundary: x=0 is an excluded vertical asymptote, so the interval begins with a parenthesis.
B
Domain: (−∞,0]. Connected rows: increasing on (−∞,0]. Empty category: no decreasing interval. Boundary: x=0 is an included right endpoint at (0,4).
C
Domain: [0,∞). Connected rows: increasing on [0,∞). Empty category: no decreasing interval. Boundary: x=0 is an included endpoint at (0,4), so the interval begins with a bracket.
D
Domain: [0,∞). Connected rows: decreasing on [0,∞). Empty category: no increasing interval. Boundary: x=0 is an included endpoint at (0,4), so the interval begins with a bracket.
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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 Label monotonicity on every connected domain interval
