1. 3.6-1 Combining Functions

2. If we have multiple functions, we can combine them/evaluate them at values, to produce a single value
The combination can be produced by just using numbers

3. Addition/Subtraction
Let f and g be two functions
A) (f + g) (x) = f(x) + g(x)
Ex. (f + g) (1) = f(1) + g(1)
B) (f – g) (x) = f(x) – g(x)
Ex. (f – g) (-1) = f(-1) – g(-1)

4. Multiplication/Division
Let f and g be two functions
C) (fg) (x) = f(x)g(x)
Ex. (fg) (-3) = f(-3)g(-3)
D) (f/g)(x) = f(x)/g(x)
Ex. (f/g)(5) = f(5)/g(5)

5. We do not necessarily need to know the actual function
We just need to know the function values for f(x) and g(x)
Graphs
Sets of ordered pairs
Function itself
Values for f(x) and g(x)

6. Example. Given that f(-3) = 15 and g(-3) = -4, find:
1) (f + g)(-3)
2) (f – g)(-3)
3) (fg) (-3)
4) (f/g)(-3)

7. Example. Given the following, find (fg)(-3) and (f + g)(-3).

8. Finding Formulas
If we need to find a new formula, we simply will look to combine the functions using the correct operation
Distribute
Check for properties of exponents
Combine like terms

9. Example. Find the formula and domain for (f + g) and (f/g) given the following two functions.
f(x) = x – 3
g(x) = x2

10. Example. Evaluate (f + g)(10) and (fg)(1) given the following two functions.
f(x) = 1/x2
g(x) = 2x + 3

11. Assignment
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1-29 odd