Function

Function

Lesson park

What is a Function?

A function relates an input to an output.

It is like a machine that has an input and an output.

And the output is related somehow to the input.

Input, Relationship, Output

• We will see many ways to think about functions, but there are always three main parts:

• The input

• The relationship

• The output

Example: 

"Multiply by 2" is a very simple function.

Here are the three parts:

Some Examples of Functions

• x2 (squaring) is a function

• x3+1 is also a function

• Sine, Cosine and Tangent are functions used in trigonometry

• and there are lots more!

Names

First, it is useful to give a function a name.

The most common name is "f", but we can have other names like "g" ... or even "marmalade" if we want.:

We say "f of x equals x squared"

what goes into the function is put inside parentheses () after the name of the function:

So f(x) shows us the function is called "f", and "x" goes in



And we usually see what a function does with the input:

f(x) = x² shows us that function "f" takes "x" and squares it.

A Function is Special

But a function has special rules:

It must work for every possible input value And it has only one relationship for each input value

This can be said in one definition:

Graphing

• The Function Grapher can only handle explicit functions,

• The Equation Grapher can handle both types (but takes a little longer, and sometimes gets it wrong).

Conclusion

• a function relates inputs to outputs

• a function takes elements from a set (the domain) and relates them to elements in a set (the codomain).

• all the outputs (the actual values related to) are together called the range

• a function is a special type of relation where:

• every element in the domain is included, and any input produces only one output (not this or that)

• an input and its matching output are together called an ordered pair so a function can also be seen as a set of ordered pairs

Thanks for your attension

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