Prove that a function is even if and only if its graph is symmetric with respect to the y-axis.

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Equivalence of Even Functions and y-Axis Symmetry

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Show that a function \( f(x) \) is even if and only if its graph is symmetric with respect to the \( y \)-axis.

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What you need first

the definition of an even function
the definition of the graph of a function
the definition of symmetry with respect to the y-axis
how to structure an 'if and only if' proof

What this problem tests

Tests the ability to write a formal proof of an equivalence using basic definitions of functions and graphs.

This is a foundational proof in precalculus and calculus, establishing the link between the algebraic definition of an even function and its geometric interpretation.

Equivalence of Even Functions and y-Axis Symmetry

What you need first

What this problem tests

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