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, 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 – 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, 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 – 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, 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)) = (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. Use the given value of k to complete the direct variation table. x 2 4
Practice
Use the given value of k to complete the direct variation table.
a. k = 3 b. k = ½ x 2 4 6 8 10
y=kx²

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.