Lesson Plan: Composite Functions | Nagwa Lesson Plan: Composite Functions | Nagwa

Lesson Plan: Composite Functions Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to form a composite function by composing two or more functions.


Students will be able to

  • understand the definition of a composite function,
  • recognize notation for function composition,
  • form a composite function 𝑓(𝑔(𝑥)) using two given functions 𝑓 and 𝑔,
  • form a specified composite function involving more than two functions (or by composing a single function with itself),
  • understand that, in general, function composition is not commutative,
  • find the domain and range of a composite function,
  • evaluate a composite function at a given value of 𝑥 when given the two (or more) original functions algebraically or graphically or when relevant values of both are given.


Students should already be familiar with

  • finding the domain and range of a function.


Students will not cover

  • finding the inverse of a function,
  • combining functions (using addition, subtraction, multiplication, or division).

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