A function is a rule that takes an input, does something to it, and gives a unique corresponding output.
There is a special notation (called ‘function notation’) that is used to represent this situation:
The notation ‘ $f(x)\,$’ is read aloud as: ‘ $f$ of $\,x\,$ ’.
So, what exactly is
$\,f(x)\,$?
Answer: It is the output from the function $\,f\,$ when the input is $\,x\,\,$.
As a second example, what exactly is
$\,g(t)\,$?
Note that
$\,f\,$ and
$\,f(x)\,$ are different :
It is often helpful to think of a function as a ‘box’. 
a function box input: $x$ name of function: $f$ output: $f(x)$ 
The letter $\,f\,$ is commonly used as the name of a function, since it is the first letter in the word function.
If
$\,\,x\,\,$ is dropped in the top of the box labeled
$\,f\,$,
then
$\,f(x)\,$ comes out the bottom.
If
$\,\,t\,\,$ is dropped in the top of the box labeled
$\,g\,$, then
$\,g(t)\,$ comes out the bottom.
If
$\,x+2t\,$ is dropped in the top of the box labeled
$\,h\,$, then
$\,h(x+2t)\,$
(read as ‘
$h$ of
$x+2t$ ’) comes out the bottom.
The equation
‘$\, f(x) = x + 2\,$’ is function notation that describes the following situation:
a function named $\,f\,$ acts on an input (here, indicated by $\,x\,$), and gives the output $\,f(x)\,$, which is equal to $\,x+2\,$.
Thus,
‘$\, f(x) = x + 2\,$’ describes the ‘ add $2$ ’ function.
This same function
$f$ could also be described by any of these:
$f(t) = t + 2$
$f(w) = w + 2$
$f(u) = u + 2$
The variable used locally to give a name to the input is called a dummy variable.
In the equation
$\,f(t) = t + 2\,$, the dummy variable is
$\,t\,$.
In the equation
$\,f(w) = w + 2\,$, the dummy variable is
$\,w\,$.
In the equation
$\,f(u) = u + 2\,$, the dummy variable is
$\,u\,$.
CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.However, you can check to see if your answer is correct. 
PROBLEM TYPES:
