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FUNCTION OPERATIONS Just like with numbers, we have operations we can do with functions. There are three main ones: Subtraction Addition Composition ADDITION This is typically represented as f(x) + g(x). If f(x) = x2 – 4x +6 and g(x) = 3x2 – 7 x +3, then f(x) + g(x) = (x2 – 4x +6) + (3x2 – 7 x +3) = 4x2 – 11x +9 You try it: f(x) = x3 – 4x +17 and g(x) = x2 + 6x – 8 f(x)+ g(x) = SUBTRACTION This is typically represented as f(x)-g(x). If f(x) = x2 – 4x +6 and g(x) = 3x2 – 7 x +3, then f(x)-g(x) = (x2 – 4x +6) – (3x2 – 7 x +3) = -2x2 + 3x +3 You try it: f(x) = x3 – 4x +17 and g(x) = x2 + 6x – 8 f(x)-g(x) = COMPOSITION This can be represented two ways: (fg)(x) or f(g(x)) What this means, essentially, is that you are plugging one function INSIDE the other. If f(x) = x2 + 4x and g(x) = x – 3, then f(g(x)) = (g(x))2 + 4g(x) = (x – 3)2+ 4(x – 3) You try it: f(x) = x3 – 4x +17 and g(x) = x2 + 6x f(g(x)) = (gf)(x) = f(x) = axb This is a power model! Note that it is just a direct variation model where the x-value has been raised to a power. a is called the constant coeffiecent x is the base b is a constant. HOW DO WE USE THESE??? Power models are often used to describe a set of data (i.e. We often put the table of values into our calculator, and then use a ‘best fit’ model. PRACTICE Use the given value of k to complete the direct variation table. x 2 4 6 8 10 y=kx² a. k = 3 b. k = ½ PRACTICE F is jointly proportional to r and the third power of s. F = 4158 when r = 11 and s=3. Find the mathematical model.