Problem preview

F-BF.3 Warmup M2-016-A13-V02

Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.

Transform a function table using a given rule

Problem

Transform the source table for \(g(x)=f(x-2)\). Explain why the inside subtraction shifts points right \(2\), write the map from a point on \(f\) to a point on \(g\), list all mapped points, and verify \(g(2)=f(0)\).

Answer choices

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Shift vertically up 2: (x, y) → (x, y+2), giving (−1, 3), (0, 2), and (1, 3).

Stretch horizontally by 2: (x, y) → (2x, y), giving (−2, 1), (0, 0), and (2, 1).

Shift horizontally right 2: (x, y) → (x+2, y), giving (1, 1), (2, 0), and (3, 1).

Shift horizontally left 2: (x, y) → (x−2, y), giving (−3, 1), (−2, 0), and (−1, 1).

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Curriculum context

Course: Math II
Standard: F-BF.3
Category: Functions
Domain: Building Functions
Objective: Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Problem type: Transform a function table using a given rule