Problem preview

F-BF.3 Warmup M3-019-A12-V03

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

Classify a function as even, odd, both, or neither

Problem

If a graph is symmetric about the origin, is the function even, odd, both, or neither?

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It is neither because symmetry about the origin is a graph feature and does not tell you whether the function is even or odd.

It is even because any kind of symmetry means the outputs match on both sides, so f(-x) = f(x).

It is odd because symmetry about the origin means points come in opposite pairs, so the function satisfies f(-x) = -f(x).

It is both even and odd because a symmetric graph must satisfy every symmetry rule at the same time.

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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: Classify a function as even, odd, both, or neither