Let's begin by looking at an example:
At a store the carrots cost $2.50/lb. The prize the customer
pays is dependent on how many pounds of carrots that he buys.
Another way to say this is to say that the total cost is a function
of the pounds bought. We can write this as an equation.
or
A function is an equation which shows the relationship between
the input x and the output y and where there is exactly one output
for each input. Another word for input is domain and for output the
range. As we stated earlier the prize the costumer has to pay, y,
is dependent on how many pounds of carrots, x, that the customer
buys. The number of pounds bought is called the independent
variable since that's what we're changing whereas the total prize
is called the dependent variable since it is dependent on how many
pounds we actually buy.
Input variable = Independent variable = Domain
Output variable = Dependent variable = Range
Functions are usually represented by a function rule where you
express the dependent variable, y, in terms of the independent
variable, x.
You can represent your function by making it into a graph. The
easiest way to make a graph is to begin by making a table
containing inputs and their corresponding outputs. Again we use the
example with the carrots
Input, x (lb)

Output, y ($)

0

0

1

2.50

2

5.00

3

7.50

A pair of an input value and its corresponding output value is
called an ordered pair and can be written as (a, b). In an ordered
pair the first number, the input a, corresponds to the horizontal
axis and the second number, the output b, corresponds to the
vertical axis.
We can thus write our values as ordered pairs
(0, 0)  This ordered pair is also referred to as the
origin
(1, 2.5)
(2, 5)
(3, 7.5)
These ordered pairs can then be plotted into a graph.
A pairing of any set of inputs with their corresponding outputs
is called a relation. Every function is a relation, but not all
relations are functions. In the example above with the carrots
every input gives exactly one output which qualifies it as a
function.
If you are insecure whether your relation is a function or not
you can draw a vertical line right through your graph. If the
relation is not a function the graph contains at least two points
with the same xcoordinate but with different ycoordinates.
The relation portrayed in the graph to the left shows a function
whereas the relation in the graph to the right is not a function
since the vertical line is crossing the graph in two points.
Videolesson: Write a rule for the function:
Input

0

1

2

4

5

output

4

3

2

0

1
