# Function Composition

In Algebra II we are finishing function composition and the students had a problem today that started as f(h(g(3))). Most students in the class would find g(3) first, then plug into h, and then plug into f. One student was literally writing the whole problem out as one equation and then simplifying. It worked for her first five problems. When she got to this one, students around her started to notice what she was doing and question it. She said, “I’ve been doing it this way the whole time and getting the right answers.” Intrigued, I sat down and attempted the problem using her strategy as well. I had to rework it twice to get the correct answer.

Here’s the problem: 4 – 2(3(2(3)^2-3(3)+5)) – 2|(2(3)^2-3(3)+5) – 10|. I think. What answer did you get?

So my student got the wrong answer twice and then asked the students to teacher her their strategy. She got the correct answer the first time. But that wasn’t good enough…she was determined to figure it out. She copied the problem on a piece of paper and took it with her promising me, “I’m going to figure this out!”