Problem preview

F-BF.3 Warmup M2-016-A13-V03

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

Transform a function table using a given rule

Problem

Use the table for \(f\) to build a table for \(g(x)=2f(x)\). Describe the vertical stretch, state the coordinate map, transform every point, identify why \(x\)-values stay fixed, and check \(g(2)\).

Answer choices

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Shift horizontally left 2: (x, y) → (x−2, y), giving (−4, 2), (−2, 0), and (0, 2).

Stretch vertically by 2: (x, y) → (x, 2y), giving (−2, 4), (0, 0), and (2, 4).

Stretch horizontally by 2: (x, y) → (2x, y), giving (−4, 2), (0, 0), and (4, 2).

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

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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