What a function is
Definition:
A function is a
relationship in maths between two variables, often x and y, and for every value
of x there is exactly one value of y.
The x value is referred to
as the independent variable and the y as the dependent variable.
The set of all the
possible values for the independent variable is called domain.
The set of all the
possible values for the dependent variable is called codomain or range.
You can
imagine that a function is a mathematical device that converts
one value to another in a known way. We can think of it as a machine. You feed
the machine an input, it does some calculations on it, and then gives you back
another value - the result of the calculations.
When we use functions
We use functions to describe physical, economic,
biological and sociological phenomenons. Or, we simply use them to express
mathematical relationships.
·
The
distance walked by a runner over time.
·
The
benefits of a company, depending on its sales.
·
The
area of a circle as its radius changes.
Functions
can come from a graph, from a text or from a formula in which two variables
relate to each other accurately. This last form is called the analytical
expression of the function.
The
analytical expression of a function is an equation that algebraically relates
the two variables involved.
