## Reflection: Grappling with Complexity Composition of Functions, Day 2 of 2 - Section 3: Decomposing functions

This year many students were able to find f(x) and g(x) in many different way.  This problem really demonstrates the different levels the students are in understanding the structure of a composition problem. The first answer is what I expected students to find. Most see the numerator and denominator having an x^2 so that is the g(x).

Answer 2 surprised me this year. The students that found that decided x^2 +4 was the g(x) these student then had to determine what to make f(x) so that the 4 goes away. After answer was put on the board the class checked to see if f(g(x)) gave us h(x).

The final answer came from students that are struggling with some basic algebra concepts. I am finding that these students have memorized procedures and not grasp how their is a structure to mathematics. These are the students that will need to work hard as we move to new topics.

Grappling with Complexity: Understanding structure

# Composition of Functions, Day 2 of 2

Unit 2: Functions and Piecewise Functions
Lesson 9 of 15

## Big Idea: Understanding how a composition can be separated into 2 functions develops skills necessary for calculus.

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Subject(s):
Math, composed function, Precalculus and Calculus, composition of functions, interpreting functions, operations with functions, function
40 minutes

### Katharine Sparks

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