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F-BF.3 Warmup M3-019-A14-V01

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

Compare transformed graphs in parallel feature rows

Problem

Compare \(A(x)=\sqrt{x-1}\) and \(B(x)=\sqrt{x+3}\).

Neutral card showing A of x equal to the square root of the quantity x minus one and B of x equal to the square root of the quantity x plus three, without a graph or comparison result. Open full size
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What this problem is really about

Compare transformed graphs in parallel rather than jumping directly from one equation to the other. Find each square-root endpoint and domain independently, then subtract corresponding endpoint coordinates to measure the relative move. Features unaffected by that coordinate difference—such as shape, vertical placement, and range—provide a second check on the comparison.

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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
Compare transformed graphs in parallel feature rows