# What is a function and how to introduce it? (includes an Activity)

A concept of a function is being officially introduced in different grades in different countries.

In Canada, teachers usually start calling a function a function around grades 9 - 10. In the USA it happens around grades 8 - 9. In a number of European countries the term function is already used widely by as early as grade 7.

There really is no right time to start using the term and labeling it as such. However, when students are already dealing with a concept of function in their math class and are able to comprehend its application in the real world, why not introduce the terminology and let them get used to it?

A function is a relationship between the independent and the dependent quantity, where for one input there is only one possible output. The output is essentially a function of the input.

The most basic example of function is a linear function.

There are examples of __linear functions__ all around us and they can be used to illustrate the concept to our students. There are many math websites that explain what a function is.

We do not even need to label the function as a certain type at first.

The main goal initially is to get students to understand how the relationship within a function works.

Once students have been exposed to a number of examples of a function and have grasped the idea, they can try to independently work with the concept as found in a real life situation and then explain how one or the other relation is actually a function.

Here is an example of a situation where students can investigate the application of a function.

Next, students can be introduced to the concept of a linear function and make a connection between the equations of linear functions and their word description. This helps the students develop an understanding of how words can be translated into algebraic expressions and equations, which they can then graph using tables of ordered pairs of independent/dependent variables.

One important aspect that cannot be overlooked when introducing and discussing the concept of function is which sets of inputs and outputs are possible for any given function - domain and range. Can time be negative? Does a ball reach a maximum height after it was hit and before falling back to the ground?

Here is an example of how based on a real life example students can investigate the possible restrictions on the independent and the dependent variables.

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