Even Odd or Neigher Function

As we have learned what is a function, we will know most of the time we will need to graph it out, so now we are going to start with the basic kind of feature of function.

Even Function and Odd Function

So you may have some questions such as what is even and odd means. We will start with an example to explain. let's say we have a two functions

1. f(x)=$x^{2}$
2. p(x)=$x^{3}$

The first one is f of x equals x to the power of two, the second one is p of x equals x to the power of 3. So in this example, the first one will be an even function because the biggest exponent of x is two, and two is an even number. The second one will be an odd function because the biggest exponent of x is three, and three is an odd number. So it will be very easy to know what kind of function is it because you just need to look at what kind of number is the biggest exponent of x then you can tell it is even or odd, there also could be neither function but we will talk about it later.

Properties of even function

1. Few major properties of an even function are listed below.
2. The sum of two even functions is even. The difference between the two even functions is even.
3. The product of two even functions is even.
4. The quotient of the division of two even functions is even. The composition of two even functions is even.
5. The composition of an even and odd function is even.

Properties of odd function

1. The sum of two odd functions is odd.
2. The difference between two odd functions is odd.
3. The product of two odd functions is even.
4. The quotient of division of two odd functions is even.
5. The composition of two odd functions is odd.
6. The composition of an even function and an odd function is even.

The examples for neither function

The examples of neither function will be the Sin function and most of the functions in trigonometry. They all have a common they are repeating over time.