Combinations of Functions

# Combinations of Functions

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## Combinations of Functions

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

7. Example:

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

10. Example:

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

12. Let’s take a look graphically.

13. Find: + 4 = 5 1

14. Find: = - 4 0 + - 4

15. Find: 0 - 4 = - 4

16. Find: 3 - (- 4) = 7

17. Find: 5 x 4 = 20

18. Find: - 3 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: