Functions review

Functions Quick Notes February 05, 2013

5.2 Properties of Functions

Relations are very important in all aspects of mathematics....

In a relationship, there are two sets of elements. The first set of elementsis called the domain and the second set is called the range.

A function is a special type of relation where each element in the domain is associated to EXACTLY 1 element in the range.

We call this a 1to1 relationship.

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Bicycle

Car

Motorcycle

Tricycle

Unicycle

Is the number of wheels on a...

Is the following relationship a function?

Domain Range


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2

3

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Bicycle

Car

Motorcycle

Tricycle

Unicycle

Has this number of wheels

Is the following relationship a function?

Domain Range

In a function, one set of data is often dependent on the value of the other set. These are called independent and dependent values.

The dependent variable has elements that belong to the range.

The independent variable has elements that belong in the domain.


The Black Box...Functions are often described as "black boxes" or machines. You put something in, "stuff" happens to it, and tada, you get something else!

Input

Ouput


The Black Box...Example: Let's pretend that this "machine" calculates the value of quarters (V) depending on the number of quarter (q).

Input

Ouput

The equation is:

Function notation allows use to show the relationship between V and q in such a way that it shows that V is in fact the dependent variable.

Function Notation:


Any function that can be written as an equation in two variables can be written in function notation.

Example:Equation: d = 4t + 5Function Notation:

Domain: ________________ Range: __________________




If there is no context, then x is the independent variable and y is the independent variable. We use the letter f for for the function notation.

Equation:

Function Notation:


Properties of a graph can provide information about a given situation

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Functions review