What are you required to know about functions? That might affect the depth and breadth of any explanations. In terms of the basic defintion, a function is any operation on a variable
x such that for any given value of
x there is only one resulting output of the operation.
In other words, given some value
x, a function of
x is an operation
f(x) such that the outcome
y=f(x) is unique. For example:
f(x)=x^2 is a function since for any value of
x there is a unique value for the result.
f(x)=sqrt(x) is not a function as it is defined here, since the result of any operation on
x is not unique. e.g. sqrt(4)=+2 or -2.
f(x)=sin(x) is a function since there is only one possible result for a given value of
x.
The
domain of a function is the set of permissible values of
x. For example:
the domain of
f(x)=x^2 is all of the real number line.
the domain of
1/x is all of the real number except for x=0.
The
range of a function is set of all possible values of
f(x) given the domain.
For example, the range of
f(x)=x^2 is the set of all real numbers greater than or equal to zero (ignoring complex values for
x for the time being.)
You could also try the following explanation:
http://mathworld.wolfram.com/Function.htmlThe scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
Isaac Aasimov
