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 x^{2} - 5x + 3
Using function notation we can write this as any of the following.
f ( x ) = 2x^{2} - 5x + 3 g ( x ) = 2 x^{2} - 5x + 3
h ( x ) = 2 x^{2} - 5x + 3 R ( x ) = 2 x^{2} - 5x + 3
w ( x ) = 2 x^{2} - 5x + 3 y ( x ) = 2 x^{2} - 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