1 / 14

Function Combination Operations in Math IV

Learn how to add, subtract, multiply, and compose functions in Math IV. Discover the process and examples of combining two functions to form another function.

eyal
Télécharger la présentation

Function Combination Operations in Math IV

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. Warm- UP F(x) = x + 2, g(x) = -x + 3 • Add the two functions • Subtract the two functions • Multiply the two functions

  2. Math IV Lesson 4 Essential Question: How do you combine two functions to form another functionSection objectives: Students will learn how to find the sum, difference, product, quotient, and composition of two functions. Standards:MM4A4. Students will investigate functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

  3. 1.5 Combinations of Functions Sum of functions (f + g) (x) = f(x) + g(x) Difference of functions (f – g) (x) = f(x) – g(x) Product of functions Fg(x) = f(x) g(x)

  4. Finding the sum of 2 functions If f(x) = 2x + 1, and g(x) = x2 + 2x – 1 Find (f+g) (x) when x = 2 (f + g) (x) = f(x) + g(x) = 2x + 1 + x2 + 2x – 1 = x2 + 4x Now plug in 2 (2)2 + 4(2) = 4 + 8 = 12

  5. Finding the difference of two functions If f(x) = 2x + 1 , and g(x) = x2 + 2x – 1 Find (f – g)(x) when x = 2 (f – g) (x) = f(x) – g(x) = 2x + 1 – (x2 + 2x – 1) = 2x + 1 - x2 - 2x + 1 = - x2 + 2 Now plug in 2 -(2)2 + 2 = -4 + 2 = -2

  6. Finding the Product of two functions Given f(x) = x2 and g(x) = x – 3 Find fg(x) when x = 4 fg(x) = f(x) g(x) = (x2) (x-3) = x3 – 3x2 Now plug in 4 (4)3 – 3(4)2 = 16

  7. Finding the quotient of two functions Given f(x) = √(x) and g(x) = √(4-x2). Find f/g(x) f/g (x) = f(x) / g(x) = √(x) / √(4-x2)

  8. Compositions of functions The composition of the function f with the function g is (f ◦ g) (x) = f(g(x)) Here you plug one function into another function. Always plug the right function into the left.

  9. Examples • Given f(x) = x + 2, and g(x) = 4-x2 • Find (f◦g)(x) when x = 2 2. Find (g◦f) (x) when x = 1

  10. Another Example • Given f(x) = x2 – 9 and g(x) = √(9-x2) • Find (f◦g)(x)

More Related