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Combining Functions

Combining Functions. Lesson 5.1. Functions to Combine. Enter these functions into your calculator. Combining Functions. Consider the following expressions Predict what will be the result if you graph. Combining Functions. Turn off the two original functions (F4)

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Combining Functions

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  1. Combining Functions Lesson 5.1

  2. Functions to Combine • Enter these functions into your calculator

  3. Combining Functions • Consider the following expressions • Predict what will be the result if you graph

  4. Combining Functions • Turn off the two original functions (F4) • Use them in theexpression for thecombined function • How does this differ from a parabola?

  5. Application • Given two functions having to do with population • P(x) is the number of people • S(x) is the number of people who can be supplied with resources such as food, utilities, etc. • Graph these two functions • Window at 0 < x < 100 and 0 < y < 1000

  6. Population and Supply • Viewing the two functions • Population • Supply • What is the significance of S(x) – P(x) • What does it look like – graph it

  7. Population and Supply • What does it mean? • When should we be concerned?

  8. Population and Supply • Per capita food supply could be a quotient • When would we be concerned on this formula?Set window-5 < y < 5

  9. Combinations Using Tables • Determine the requested combinations

  10. Assignment A • Lesson 5.1A • Page 378 • Exercises 1 – 37 EOO

  11. Composition of Functions • Value fed to first function • Resulting value fed to second function  • End result taken from second function 

  12. Composition of Functions • Notation for composition of functions: • Alternate notation:

  13. Try It Out • Given two functions: • p(x) = 2x + 1 • q(x) = x2 - 3 • Then  p ( q(x) ) = • p (x2 - 3) = • 2 (x2 - 3) + 1 = • 2x2 - 5 • Try determining  q ( p(x) ) 

  14. Try It Out • q ( p(x) ) = • q ( 2x + 1) = •   (2x + 1)2 – 3 = •    4x2 + 4x + 1 – 3 = •    4x2 + 4x - 2 

  15. Using the Calculator • Given • Define these functions on your calculator

  16. WHY ?? Using the Calculator Now try the following compositions: • g( f(7) ) • f( g(3) ) • g( f(2) )                • f( g(t) ) • g( f(s) )

  17. Using the Calculator • Is it also possible to have a composition of the same function? • g( g(3.5) ) = ???

  18. Composition Using Graphs Do the composition of k( j(x) )

  19. Composition Using Graphs • It is easier to see what the function is doing if we look at the values ofk(x), j(x), and then k( j(x) ) in tables:

  20. Composition Using Graphs • Results of k( j(x) )

  21. Composition With Tables • Consider the following tables of values: 

  22. Assignment B • Lesson 5.1B • Page 380 • Exercises 57 - 77 EOO 95, 97 • Assign the Composition of FunctionsGeogebra WorksheetDue in 1 Week

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