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Identifying Functions
First off, what is a function?
A function is a relation in which each input item/value has only one output item/value.
What is a relation?
A relation is the relationship between variables (x and y or in this case, input and output).
This diagram below demonstrates the relationship
between functions and relations. Not all
relations are functions, but all functions are relations.
What is an input?
Also known as the independent value, an input is the item/value that you put into an expression.
Helpful Tip: You always begin with the input item/value.
What is an output?
The output item/value depends on the input item/value.
Helpful Tip: The output item/value is the solution to the function.
Look at the chart below:
Let’s look at functions in relation to numbers.
Input Output
-8 -14
18 -14
20 7
Is this relation a function?
Yes, each input value has only one output. It does not matter how many times the output value is repeated.
Input Output
-13 16
-13 4
8 5
Is this relation a function?
No, the input value of -13 has 2 output values (16 and 4). To be a function, inputs must have only one output.
The relationship between the domain and range or input and outputs that don’t form functions are still relations as the diagram above demonstrates.
Helpful Tip: To determine whether the input and
output items/values are function, each input must be assigned to only one output.