# File ```FUNCTION OPERATIONS
Just like with numbers, we have operations we
can do with functions.
There are three main ones:
Subtraction
Composition
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: (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) =
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=kx&sup2;
a. k = 3
b. k = &frac12;
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.
```