Arithmetic Combinations of Functions

Two functions can be combined to make new functions, this is called arithmetic combinations of functions. Say you have two equations...

 f (x) = 3x - 7   and   g (x) = x + 5

f (x) and g (x) both represent the y values of two different functions so these can be combined to make new functions both algebraicly and graphically

Algebraic soultion
    
     Sum:   (f + g) (x) which equals f (x) + g (x) ... so...= (3x -7) + (x + 5)
                                                                                 = 4x - 2

     Difference: (f + g) (x) which equals f (x) - g (x) ... so... = (3x-7) - (x+5)
                                                                                        = 2x - 12

     Product: (fg) (x) which equals f (x) * g (x) ... so... = ( 3x-7) (x+5)

                                   =

                                                                               
   Quotient: (f/g) (x) which equals f (x) / g (x) ... so... = (3x-7) / (x+5)
                                                                               x can't equal -5

Graphic Solution

     Very much the same as solving algebraicly. For the sum, you add the y points of each function and you get your new point. For the difference you subtratc. For product you multiply. For Quotient you divide.


                              Co-Published by Jack LaFave