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So often teaching graphing transformations of functions boils down to simply recalling facts without understanding the concepts . Maybe we started out trying to explain the conceptual understanding behind the rules, but as the test looms closer and we’re desperate for students to understand we throw our hands in the air and say “just memorize the rules!”
What if I told you there was a way to introduce the topic so that students actually developed the conceptual understanding THEMSELVES, and discovered the rules so that your lesson didn’t have to include you listing them all out?
How to Introduce Transformations of Functions
The BEST way to introduce function transformations is to allow students to play with the functions. For me that looks like this:
- Create a table of values for the parent function, say y=|x|, and then graph it.
- Then, make a table of values and graph a simple transformation, say y=|x-2|.
- What do the students notice? (AKA What’s the rule? You just found it!)
What I do is divide students into groups, and give each group a different transformation to discover. Again, all the students are doing is creating tables of values, i.e. plugging in x-values to the equation. This activity is non-intimidating and has a non-existent barrier to entry.
Once all groups have discovered their individual transformations, I have them share the rules with the other groups while they fill out a summary page.
What Functions Does This Work For?
I use this to introduce transformations of:
- Exponential Functions
- Absolute Value Functions
- Quadratic Functions
- Sine Functions
- Radical Functions
- Cubic Functions
- Cube Root Functions
You can buy all of these resources from my TpT store. Let me know if you implement this strategy in your classroom! Keep the conversation going in the comments, on IG @mathymrs.j, or through email, mathymrsj@gmail.com.
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Happy Teaching!
Natasha