1 / 22

Combining Functions

Explore the combination of functions to analyze population and supply dynamics. Graphing functions, interpret significance, and calculate compositions.

jiml
Download Presentation

Combining Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 346 • Exercises 1 – 25 odd, 61, 62

  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 347 • Exercises 27 – 77 EOO

More Related