1. Function Operations (and inverses!)

2. Function Operations • Just like with numbers, we have operations we can do with functions. • There are three main ones: • Subtraction • Addition • Composition

3. Addition • This is typically represented as f(x) + g(x). • If f(x) = x2 – 4x +6 and g(x) = 3x2 – 7 x +3, thenf(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) =

4. Subtraction • This is typically represented as f(x)-g(x). • If f(x) = x2– 4x +6 and g(x) = 3x2 – 7 x +3, thenf(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) =

5. Composition • This can be represented two ways: (fg)(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, thenf(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)) = (gf)(x) =

6. Power Models

7. 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.

8. 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.

9. Practice • Use the given value of k to complete the direct variation table. a. k = 3 b. k = ½

10. 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.