Even and odd functions both have symmetry at some point. However, they are different because even functions have y-axis symmetry and odd functions have origin symmetry. You can check if a function is even by using the equation f(x)=f(-x) because the original formula must always be equal to the equation when x is replaced with -x.
You can tell whether or not a function is odd by using the equation f(-x)=-f(x) because when x is replaced with -x, it must be equal when the function is multiplied by -1. Functions that have x raised to an even power are always even functions, and functions that are raised by an odd number are always odd functions.However, when functions are shifted from either left of right they can lose their symmetry that defines them as either odd or even. I don't really have any questions regarding this concept because it is pretty straight forward and I feel as if I actually understand this.
You can tell whether or not a function is odd by using the equation f(-x)=-f(x) because when x is replaced with -x, it must be equal when the function is multiplied by -1. Functions that have x raised to an even power are always even functions, and functions that are raised by an odd number are always odd functions.However, when functions are shifted from either left of right they can lose their symmetry that defines them as either odd or even. I don't really have any questions regarding this concept because it is pretty straight forward and I feel as if I actually understand this.