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F-BF.3 Warmup M3-019-A03-V01

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

Select reflection axes and simplify the transformed function

Problem

Analyze the transformation from \(f(x)~=~\sqrt{x}\) to \(-\sqrt{x}\). State the inside and outside effects, the resulting expression, and its domain.

Neutral reflection analysis card showing parent square root of x and expression negative square root of x, without a transformed graph, domain, or reflection classification. Open full size
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What this problem is really about

First decide whether a negative changes the input or the entire output; its location determines which coordinate is negated. Write the corresponding point map, test it on a familiar parent point, and then recheck the radical restriction. That sequence keeps the reflection description, transformed expression, and domain tied to the same structure.

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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
Select reflection axes and simplify the transformed function