Problem preview

F-BF.3 Warmup M3-019-A14-V03

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 \(A(x)=2^x+1\) and \(B(x)=3\cdot~2^x+1\).

Neutral card showing A of x equal to two raised to the x power plus one and B of x equal to three times two raised to the x power plus one, without a graph or comparison result.

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Features: both asymptotes are y=1; A(0)=2 and B(0)=4. Relative transformation: B triples vertical distance from y=1. Shared property: same exponential orientation.

Features: both asymptotes are y=1; A(0)=2 and B(0)=4. Relative transformation: B divides vertical distance from y=1 by 3. Shared property: same exponential orientation.

Features: asymptotes and points cannot be compared. Relative transformation: indeterminate. Shared property: vertical distances cannot be compared.

Features: both asymptotes are x=1; A(0)=2 and B(0)=4. Relative transformation: B triples horizontal distance from x=1. Shared property: same exponential orientation.

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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