Problem preview

F-IF.8 Warmup M3-027-A14-V02

Rewrite functions in equivalent forms to reveal and explain useful properties.

Decide whether a proposed rewrite keeps the same function and the same restrictions

Problem

Does this rewrite preserve the original restrictions: \(\sqrt{(x-1)^2}\) rewritten as \(x-1\)?

Answer choices

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No; the rewrite is invalid because square roots require x-1 ≥ 0, so the original expression already has the restriction x ≥ 1.

Yes; squaring and then taking the square root cancels completely, so √((x-1)²) is always x-1 on the original domain.

Yes; the rewrite preserves the restriction because x-1 and |x-1| have the same values on both sides of x = 1.

No; over all real numbers, √((x-1)²) is |x-1|, so rewriting it as x-1 only works if the domain is restricted to x ≥ 1.

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Curriculum context

Course: Math III
Standard: F-IF.8
Category: Functions
Domain: Interpreting Functions
Objective: Rewrite functions in equivalent forms to reveal and explain useful properties.
Problem type: Decide whether a proposed rewrite keeps the same function and the same restrictions