## Reflection: Developing a Conceptual Understanding Graphing y=a/(x-b)+c - Section 2: Investigation and New Learning

I wanted to talk more about the b tells you the vertical asymptote and c tells you the horizontal asymptote." This is obviously accurate for functions in this form, but it is not very meaningful--almost anybody could figure this out without understanding the functions too well, after just looking at a few equations and their graphs.

I really want students to be able to explain why this generalization holds, and I have recently realized that if I don't teach them why, they won't know or be able to explain this. I created the choose inputs scaffold to help students think in different ways about how the function rule itself relates to the asymptotes. The more I tried to create scaffolds to help students think about these connections, the more complicated I realized the connections were. I wanted students to understand how to choose inputs to get really big outputs, and to explain what kinds of outputs would result from really big inputs. Then, I wanted them to identify these points on the graph, and connect these points to the asymptotes. Finally, I wanted them to be able to describe these asymptotes with approach statements.

The deeper we got into this learning target, the more scaffolds I wanted to create to help students make those connections.

Developing a Conceptual Understanding: Building a Deeper Conceptual Understanding

# Graphing y=a/(x-b)+c

Unit 6: Rational Functions
Lesson 5 of 10

Print Lesson