To expand: The
property f(x) = f(-x) means that
graphs of even functions are
symmetric when
reflected in the
y-axis.
This is a very
distinctive feature which allows the
evenness of
even functions to be recognised at a
glance!
The fact that
any function can be represented as the sum of an even function and an odd one is very important in many branches of
mathematics, most notably in
Fourier analysis.