Algebra 2 Operations With Functions
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What's So Good About F(X)?
Operations With Functions

 

 Well for one thing, it let's you do stuff like this:

 

 If F(X) = 3X2 + 5  what is F(2)?

 
 This means, take whatever is inside the parenthesis ()
 and substitute it for X, 
 then work the problem ...
 
  F(X) = 3X2 + 5
  F(2) = 3(2)2 + 5
  F(2) = 3(4) + 5
  F(2) = 12 + 5
  F(2) = 17
 
 Try another one ...
 

 If F(X) = 5X3 - 3X2 + 2  what is F(W)?

 
 OK, this one looks weird and scary,
 but just put what in inside the parentheses in for X
 and work the problem (if you can)
 
  F(X) = 5X3 - 3X2 + 2
  F(W) = 5W3 - 3W2 + 2
 
 And we're done.
 The thing to remember is 
 whatever is inside the parenthesis gets put in for the variable
 named inside the F( )
 
 So:

 If F(X) = 3X4 - 2X + 5  what is F(platypus)?

 
 Who knows what this means! just go through the process ...
 
  F(X) = 3X4 - 2X + 5
  F(platypus) = 3(platypus)4 - 2(platypus) + 5
 
 Let's try one more ...
 

 If F(X) = 5X2 - 2X + 3  what is F(3W2 - 5)?

 
 Yeah it's going to be a little messy, 
 but just plug and chug ...
 
  F(X) = 5X2 - 2X + 3
  F(3W2 - 5) = 5(3W2 - 5)2 - 2(3W2 - 5) + 3
  F(3W2 - 5) = 5(9W4 - 30W2 + 25) - 6W2 + 10 + 3
  F(3W2 - 5) = 45W4 - 150W2 + 125 - 6W2 + 13
  F(3W2 - 5) = 45W4 - 156W2 + 138
 
 Remember F(X) is just another name for Y.
 Since we can put stuff into the little parenthesis
 we can do more with an F(X)  than we can with a dumb old Y.
 
 Is F(X)  the only other name Y has?
 
 Not a chance! It can also use:
 

 G(X)   or H(X)   or   K(X) 

 
 or 

 ANY LETTER(X) 

 
 In general, we try to pick letters in the middle of the alphabet
 for function names.
 
 We also try to pick letters near the end of the alphabet for variables 
and letters near the beginning for constants.
 

   copyright 2005 Bruce Kirkpatrick

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