Problem preview

F-IF.7.b Warmup M2-022-A06-V02

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.

Derive radical-function domain and range

Problem

Determine the domain and range of \(y=-\sqrt{x+1}+5\).

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family=square-root; input condition=x+1≥0; solved condition=x≥-1; endpoint=(-1,5); output direction=y≥5 because reflection is ignored; domain=[-1,∞); range=[5,∞)

family=square-root; input condition=x+1≥0; solved condition=x≥-1; endpoint=(-1,5); output direction=y≤5; domain=[-1,∞); range=(-∞,5]

family=square-root; input condition=x≥5 from vertical shift; solved condition=x≥5; endpoint=(5,5); output direction=y≤5; domain=[5,∞); range=(-∞,5]

family=square-root; input condition=x+1>0; solved condition=x>-1; endpoint=(-1,5) excluded; output direction=y<5; domain=(-1,∞); range=(-∞,5)

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Curriculum context

Course: Math II
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: Derive radical-function domain and range