# Writing Functions

a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range). Here you will learn more about writing a function.

A function is a process or relation that associates each element ‘$$a$$’ of a non-empty set $$A$$ with at least one single element ‘$$b$$’ of another non-empty set $$B$$.

Each function consists of input and output. An input is a variable that enters a function, which is also called an independent variable or domain. The output is the variable that comes out of the function, and it is also called the dependent variable or range.

A function in math can be represented as:

• a set of ordered pairs
• an arrow diagram
• a table form
• a graphical form

## How to Write a Function with an Ordered Pairs Table

Step 1: Analyze the first set of input-output pairs. Identify one solution using addition and another using multiplication.

Step 2: Verify the solutions from Step 1 with the next set of pairs. Repeat this process with additional pairs until only one solution remains consistent.

Step 3: Once a single solution is determined, check all remaining pairs to confirm the rule applies to all of them.

Step 4: Write the function rule as either $$f(x) = x + c$$ for addition or $$f(x) = cx$$ for multiplication, where $$c$$ is the constant used in the established rule.

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