1. SAT Problem of the Day

2. 2.4 Operations With Functions
Objectives:
Perform operations with functions to write new functions
Find the composition of two functions

3. Operations With Functions
For all functions f and g:
(f + g)(x) = f(x) + g(x)
Sum
Difference
(f – g)(x) = f(x) – g(x)
Product
(f  g)(x) = f(x)  g(x)
where g(x)  0
f(x)
g(x)
Quotient

4. Example 1 Let f(x) = 4x2 + 6x – 9 and g(x) = 6x2 – x + 2.
a) Find f + g.
(f + g)(x) = f(x) + g(x)
= (4x2 + 6x – 9) + (6x2 – x + 2)
= 10x2 + 5x – 7
b) Find f - g.
(f - g)(x) = f(x) - g(x)
= (4x2 + 6x – 9) - (6x2 – x + 2)
= -2x2 + 7x – 11

5. Example 2 Let f(x) = 9x2 and g(x) = 4x + 3. a) Find f · g.
(f · g)(x) = f(x) · g(x)
= 9x2(4x + 3)
= 36x3 + 27x2
b) Find
where

6. Practice Let f(x) = 4x2 – 2x + 1 and g(x) = -5x. Find: f + g f – g

7. Composition of Functions
Let f and g be functions of x.
The composition of f with g, denoted f ○ g, is defined by f(g(x)).
The composition of g with f, denoted g ○ f, is defined by g(f(x)).

8. Example 3 Let f(x) = x2 + 4 and g(x) = 2x. a) Find = g(x)2 + 4 b) Find

9. Example 4 Let f(x) = 2x2 +3x - 5 and g(x) = 4. a) Find
= 2(g(x) 2) + 3g(x) – 5
b) Find

10. Practice 1) Let f(x) = -2x2 + 3 and g(x) = -2x. Find

11. Homework
Page 115 Exercises 13, 21, 30-34, odd, 60-63

12. 6 minutes
Warm-Up (WID)
Make up a word problem like the ones on the composite function worksheet. Be sure to take all the right steps: define the scenario, define your variables clearly, and then show the (composite) functions that relate the variables.