A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
This means that if the object x
x
is in the set of inputs (called the domain) then a function f
f
will map the object x
x
to exactly one object f(x)
f
(
x
)
in the set of possible outputs (called the codomain).
The notion of a function is easily understood using the metaphor of a function machine that takes in an object for its input and, based on that input, spits out another object as its output.
Example: 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!
But we are not going to look at specific functions ...
... instead we will look at the general idea of a function.