Graph of Even Function is Symmetrical about y-Axis

Theorem

Let $f$ be an even real function.

Let the graph $G$ of $f$ be presented in a Cartesian plane.

Then $G$ is bilaterally symmetric whose axis of symmetry is the $y$-axis.

Proof

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Sources

• 1973: G. Stephenson: Mathematical Methods for Science Students (2nd ed.) ... (previous) ... (next): Chapter $1$: Real Numbers and Functions of a Real Variable: $1.3$ Functions of a Real Variable: $\text {(h)}$ Even and Odd Functions
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): even function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): even function