What Is Function Notation?
Another topic in advanced algebra is function notation. So first of all, I’ll say, the
value of any algebraic expression of x depends on the value of x itself.
So for example, here are four different expressions. We could plug in different
values of x and of course any input value of x would produce different outputs in
each of these four expressions.
And of course with x–with the expression 1 over x–we can’t plug in 0 but we can
plug in any other number on the other line. For the other three we could plug in any
number on the number line. We can plug in positive numbers, negative numbers, or
fractions. And of course we’d get all kinds of different outputs if we plugged in
different inputs. So, changing the value of x, of course, changes the value of the
expression.
Function notation is a way to formalize this process.
Image by Elena100
Function Discussion
A function is like a machine that takes an input and assigns it to an output. Different
inputs give the same or different outputs. For the purpose of the test, a function is
always associated with an algebraic expression. The input is the value of x we are
going to plug in and the output is the value of the expression once we plug in that
value of x.
So function notation, for a function with the name f, we write it this way. We write f,
and then we write the x in parentheses. This is read f of x. And this is not
multiplication. We are not taking a number f and multiplying by the number x. F is
technically what is called an operator it is performing an operation on x.
