Function notation: Next we have to take a rapid look at function notation. Function notation is nothing more than way of writing the y in a function which will let to simplify notation and some of our work a little.

Let's take a look at the given function.

                    y = 2 x² - 5x + 3

Using function notation we can write this as any of the following.

f ( x ) = 2x² - 5x + 3                                       g ( x ) = 2 x² - 5x + 3

h ( x ) = 2 x² - 5x + 3                                     R ( x ) = 2 x² - 5x + 3

w ( x ) = 2 x² - 5x + 3                                     y ( x ) = 2 x² - 5x + 3

Remember again that it is not a letter times x, it is just a fancy way of writing y. hence, why is this useful? Well let's take the function above & get the value of the function at x=-3.  By using function notation we represent the value of the function at x=-3 as f(-3).  Function notation provides us a nice compact way of representing function values.

Now, how do we in fact evaluate the function? That's actually simple.  Everywhere we illustrate an x onto the right side we will substitute whatever is in the parenthesis on the left side. For our function it gives,

                   f ( -3) = 2 ( -3)²  - 5 ( -3) + 3

                             = 2 (9) + 15 + 3

                               = 36