A function is a rule that takes an input, does something to it, There is a special notation (called ‘function notation’) that is used to represent this situation:
What exactly is
$\,f(x)\,$?
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’. 

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
$\quad f(x) = x + 2\quad$ 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,
$\quad f(x) = x + 2\quad$ 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
$\,f(x) = x + 2\,$, the dummy variable is
$\,x\,$.
In the equation
$\,f(t) = t + 2\,$, the dummy variable is
$\,t\,$.
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:
