Before our break I created a set of challenges for students to investigate translations of different functions. I had a few goals in mind:

- Introduce a few basic functions that we will work with in this unit (square root, rational, cubic, quadratic).
- See how certain points on the function are translated.
- How does affecting the values in the equation affect the graph of a
**variety**of functions? - Use function notation to represent translations.

## Challenges:

First – Learn about the square root function & see how a function is translated vertically.

We had a class discussion on which points they picked and how those points changed in the function f(x) + 3.

They are then led down a **Desmos Trail** to complete a few mini-challenges trying their knowledge of using function notation and vertical translations matching the “home” function to the translated one. Each challenge then links to the next!

We did the same for challenge 2, the basic rational function, and horizontal translations. The handout served as our class note.

After our discussions the **Desmos Trail** continues, starting at challenge 3 until challenge 9. Each testing our knowledge of equations and translations. You may also see I threw in a few reflections in there too!

Here are a few students working away on the challenges.

## Direct Links:

- Challenge 1 | miniA | miniB | — Square Root Function
- Challenge 2 | miniA | miniB | — Rational Function
- Challenge 3 – Cubic Function
- Challenge 4
- Challenge 5
- Challenge 6
- Challenge 7
- Challenge 8
- Challenge 9 – Multiple

Big thanks to Mary Bourassa for tips and fixes and to Michael Fenton for creating Match my Parabola and later pointing me to his own transformation challenges. Hail #MTBOS

**Next up in our class** — Going down the rabbit hole a little further…..Stretches and Compressions Challenge