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F-BF.3 Warmup M3-019-A04-V03

Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.

Analyze a transformed radical graph with anchor, domain, and range

Problem

Analyze \(y~=~\sqrt[3]{x~-~4}~+~5\) relative to \(y~=~\sqrt[3]{x}\). State the transformations, central inflection, domain, and range.

Neutral cube-root-transformation card showing only the cube root of the quantity x minus four, plus five outside the cube root; no graph features are shown.
Use the center anchor to read the translation, then notice that the cube-root S-shape keeps extending left and right.
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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-BF.3
Category
Functions
Domain
Building Functions
Objective
Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Problem type
Analyze a transformed radical graph with anchor, domain, and range