1. Combinations of Functions

2. Objective
To be able to perform operations and combinations of functions algebraically, graphically, and with the use of technology.

3. Relevance
To be able to model a set of raw data after a function to best represent that data.

4. Warm Up – Graph the piecewise function.

5. Operations with Functions:
Sum
Difference
Product
Quotient

6. Example: Let f(x) = 5x² -2x +3 and g(x) = 4x² +7x -5
Find f + g
Find f - g

7. Example:

8. Using your GDC
Start with “VARS”

9. Example: Let f(x) = 5x² and and g(x) = 3x – 1.
Find f · g
Find f/g

10. Example:

11. Example: f(x)=2x + 3 and g(x) = x -7

12. Let’s take a look graphically.

13. Find: 1 + 4
= 5

14. Find:
- 4
= - 4

15. Find: 4
= - 4

16. Find:
(- 4)
= 7

17. Find:
5 x 4
= 20

18. Find: x 5
= - 15

19. Find: 6 3
= 2

20. Composition of Functions

21. A composite function is a combination of two functions.
You apply one function to the result of another.

22. The composition of the function f with the function g is written as f(g(x)), which is read as ‘f of g of x.’
It is also known as which is read as ‘f composed with g of x.”
In other words:

23. Ex: f(x)=2x + 5 and g(x) = x - 3
You can work out a single “rule” for the composite function in terms of x.

24. Do you think will give you the same result?
NO!

25. You Try….
f(x) = 2x + 2
g(x) = (x + 2)2
Find:

26. You may need to evaluate a composite function for a particular value of x.
Method 1:
Work out the composite function.
Then substitute 3 for x.

27. You may need to evaluate a composite function for a particular value of x.
Method 2:
Substitute 3 into g(x).
Substitute that value into f(x).

28. Now, let’s take a look at it graphically……

29. Find:

30. Find:

31. Find:

32. Find:

33. Find: