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Messier Notation

OK, so we're cool with the easy notation like

f( x ) = x^2 + 5

Sof( 3 ) = ( 3 )^2 + 5 = 9 + 5 = 14

f( -2 ) = ( -2 )^2 + 5 = 4 + 5 = 9
              These ( ) are killer important!

What if we let x = k?

We'd getf( k ) = k^2 + 5

That wasn't so bad... but, they get worse!

What wouldf( x + h )be?

Let's get your brain thinking the right way...  Then it will be easy!

f( x ) = x^2 + 5

Think of it as

f( blob ) = ( blob )^2 + 5

This function guy takes any blob... squares it... then adds 5!  So...

f( karen ) = ( karen )^2 + 5 ... f( coolmath ) = ( coolmath )^2 + 5 ... f( booger ) = ( booger )^2 + 5 ... f( x + h ) = ( x + h )^2 + 5

Whoa, dude!  You just got tricked into doing one of the hardest things in Algebra!

If f( x ) = x^2 + 5

                         then f( x + h ) = ( x + h )^2 + 5 ... = x^2 + 2xh + h^2 + 5 ... clean it up!