Part 2/5:
In the graphical representation, even functions exhibit symmetry about the y-axis. This means that for every point on the function curve in the positive x-domain, there is a corresponding point at the same distance in the negative x-domain.
Graphical Example of Even Functions
A classic example of an even function is:
[ f(x) = x^2 ]
When substituting ( -x ) into the function, we find:
[ f(-x) = (-x)^2 = x^2 ]
Since ( f(-x) = f(x) ), we can conclude that ( f(x) = x^2 ) is an even function. Its graph, a parabola, is symmetric about the y-axis.
Odd Functions
On the contrary, an odd function is characterized by a different relationship:
[ f(-x) = -f(x) ]