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Function Notation

So...

x guys go in... and f(x) guys spit out!

( f(x) is just the official output name. )

             input: x -> rule: + 1 -> output: f( x )

So, this guy...

input: 3 -> rule: + 1 -> output: 4
 

Is officially written as

f( 3 ) = 3 + 1 = 4 ... f( 3 ) = 4 ... the 3 is the domain guy ... the 4 is the range guy

What if our input is -5?

f( -5 ) = -5 + 1 = -4 ... f( -5 ) = -4

Here's another way to look at it:

We started withf( x ) = x + 1...

f(-5) is like saying "let x = -5."