- Even function: x^2
- Odd function: x^4-x
Even and odd functions are similar because when you have a table like what is shown below, the x will always change from a positive to a negative or from a negative to a positive.
They are different because the graphs of the even function will always be symmetrical. Odd functions will not have a symmetrical graph. In a graph like what is shown below, you may think that they look the same. But, even functions will not touch (0,0). Odd functions will touch (0,0).
When solving for even functions, the characteristic is for every -x value f(-x)=f(x)
In other words, you will change all of the x in your equation to a negative. When you solve for it, you will get the same equation that was given to you. Your x will be positive again.
When solving for odd functions, the characteristic is for every -x value f(-x)= -f(x)
In other words, when you change all of your x to negatives, your final equation will have the opposite signs that you had in the original equation.
One way of knowing immediately when figuring out if your equation is an even or odd function, is by the power that x is raised to. If the power is a 1,3,5,7,9,........it is an odd function.
If the x is raised to a 2,4,6,8,10,.......it is an even function.
The families of functions that will always be even are the even functions. The families of functions that will always be odd are the odd functions.