### Theory:

We can represent a function in four ways, namely:

1. Set of ordered pairs

2. Table form

3. Arrow diagram

4. Graph
1. Set of ordered pairs
In a function $$f : A \rightarrow B$$, the set of ordered pairs $$f =$$ $$\{(x, y) | y = f(x), x \in A\}$$ is a function.
Example:
The number and its square can be represented using ordered pairs as:

$$\{(1, 1), (2, 4), (3, 9), (4, 16),...\}$$
2. Table form
We can also represent the functions in the table form. Again, the preimages are on one side, while the images are on the other side.
Example:
Let us look at the same example of number and their squares in the table form.

 The number Its square $$1$$ $$1$$ $$2$$ $$4$$ $$3$$ $$9$$ $$4$$ $$16$$
3. Arrow diagram
The arrow diagram has the elements of the domain $$f$$ and their corresponding images connected by arrows.
Example:
Let us look at the numbers and their squares in the form of an arrow diagram. 4. Graph
We can also plot the elements of $$f$$ and their corresponding images on the graph.
Example:
Let us look at the example of numbers and their squares on a graph. An equation given on the graph is also called a curve.