EVEN and ODD Functions!

EVEN Function(s)

GRAPHICALLY, an even function is a function that is symmetrical about the y-axis. Meaning that Quadrant 1 & 2 or 3&4 are like a mirror view of each other. Some examples of even functions are the cos x graph or even a parabola:

What makes these graphs symmetrical about the y-axis or in other words even, is due to the algebraic form of the even functions.

ALGEBRAICALLY, an even function of x is defined as f(-x) = f(x)
- The input, whether it be negative (-x) or positive (x), will share the same output. Having said that, it would be similar to the points (-1,1) and (1,1) or (1,-1) and (-1, -1).
- The x (input) could change but the y (output) will remain the same, making the two points reflect themselves on the y-axis.

ODD Function(s)

GRAPHICALLY, an odd function is a function that is symmetrical about the origin. The graphs of sin x and f(x) = x are good examples of odd functions. Quadrant 1 & 3 or 2&4 are reflected diagonally in any odd function.




ALGEBRAICALLY, an odd function is defined as f(-x) = -f(x)
- For example, if a point (1,1) lies on a graph, then the opposite points (-1,-1) must also lie on that graph. If (-1, 1) lies on a graph then you will also find (1,-1).


I tried to explain even and odd functions using points with one unit, because that was how I was better able to understand these functions. Comment me if you have any questions.