Math Education Concepts

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It’s Just Substitution

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The figure of a composite function.

The figure of a composite function. (Photo credit: Wikipedia)

I’ve always thought that teaching lessons on the composition of functions would be easy, but I was wrong.  Each semester poses a greater challenge.  This semester is the same.  The students look at me as if they have no idea what I’m talking about when I say “it’s just substitution.”  (My basic explanation for the process of completing the composition of functions). I show examples with numerals, then with single variables, then with binomials, and so on.  They follow along until I get to binomials, then they get “confused” again.  I encourage my students to complete their homework assignments (for practice and hands on learning) and to visit me during my office hours, so I can help them.  In the end some get it, some keep trying.

In their defense, the most challenging component of my composition of functions lesson is finding the domain of the composed functions.  That’s another blog entirely.

The one bit of satisfaction I received while teaching the early part of the lesson occurred when a student yelled out “it’s just like the difference quotient, right?”  I answered, “yes, exactly, if we let g(x) = x + h.”  I felt like someone finally got it and it felt great.  I only wish all the students made the same connection.  If only…

In any event, I found a nice explanation on  It explains the composition of functions really clearly, I think.

Enjoy and pass it along!


Author: Math Education Concepts

I am a Co-founder of and Program Coordinator for Math Corps Philadelphia, a combined academic enrichment and mentoring program. I am the author of "Teacher Training Manual: Designed for Secondary Mathematics Teachers of African American Urban Students." I hold a Master of Education degree in Secondary Mathematics and have several years of experience teaching secondary and post-secondary mathematics.

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