Write the following functions on the board and ask students to describe the transformation that each function represents:
1) f(x) = (x-5)^2
2) g(x) = (x+5)^2
3) h(x) = x^2 + 5
4) j(x) = x^2 - 5
Have students work on this problem individually first and then share their work with a partner. In this case have students refrain from sharing their ideas out with the class. This is the work of the day's lesson.
Have students work with a partner of similar ability level on this project. Now that students have investigated transformations, it is their turn to show off what they know. Their goal is to build a "how to" guide for transformations of functions going both horizontally and vertically. (NOTE: in order to solidify the concept underlying these transformations they were done separately from stretching and reflecting).
Leave this project very open ended so that students will make choices that can make their work more appealing and usable (MP1). I tell students that their goal is to make a guide that could be used by a student who has not seen transformations of functions. Their guide should make the concept understandable and use multiple representations to illustrate the process of moving a function around the coordinate plane (MP3).
Ensure that students have the use of a calculator when constructing their project. This will help them to experiment with different transformations and ensure that their algebraic equations are constructed correctly (MP2) (MP7).
Ensure that students are working on this exit ticket independently. In this ticket out (transformations_how_to_close.doc) students will be using their knowledge of transformations to write the equation for each function. Based on the ability of your class you may want to tell them that the parent function is the absolute value function. However, based on the work completed in the lessons leading up to this one students should recognize this function.
As an extension, if time permits, students can also write how they determined the equation for one or all of their functions. This can be written at the bottom of the page and will give you some insight into how the students are thinking about these transformations.