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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:

  8. Using your GDC Start with “VARS”

  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: