# ALEX Lesson Plan

## Building Functions: Composition of Functions

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This lesson provided by:
 Author: Lorie White System: Lauderdale County School: Rogers High School
General Lesson Information
 Lesson Plan ID: 35604 Title: Building Functions: Composition of Functions Overview/Annotation: This lesson provides a review of evaluating functions and finding function rules as well as an introduction to the composition of functions. The review is accomplished through the use of an online exploration using a function machine. The idea of a function machine is also used to explain the composition of functions. Instruction is provided in finding the composition using several different representations of functions (input/output tables, graphs, and function rules). This lesson results from the ALEX Resource Gap Project.
Associated Standards and Objectives
Content Standard(s):
Mathematics
MA2019 (2019)
Algebra I with Probability
17. Combine different types of standard functions to write, evaluate, and interpret functions in context. Limit to linear, quadratic, exponential, and absolute value functions.

a. Use arithmetic operations to combine different types of standard functions to write and evaluate functions.

Example: Given two functions, one representing flow rate of water and the other representing evaporation of that water, combine the two functions to determine the amount of water in a container at a given time.

b. Use function composition to combine different types of standard functions to write and evaluate functions.

Example: Given the following relationships, determine what the expression S(T(t)) represents.

Function Input Output
G Amount of studying: s Grade in course: G(s)
S Grade in course: g Amount of screen time: S(g)
T Amount of screen time: t Number of follers: T(t)

Local/National Standards:

Primary Learning Objective(s):

• Students will be able to write a function rule given domain and range values.
• Students will be able to find the range values of a composition of two functions given the two function rules and a domain value.
• Students will be able to write a function rule for the composition of two functions given the function rules for the two functions.
• Students will be able to find the value of the composition of two functions given the graphs of the two functions.