Data Tables of Transformed Radical Functions

Objective

SWBAT write function rules given data tables of transformed radical functions.

Big Idea

Students examine very decontextualized data to explore transformations of radical relationships with numbers, before extending this to graphs in future lessons.

Warm-Up

30 minutes

By this time, students should have a solid understanding of problem (1) and (3) in the warmup (Transformed Radical Functions Warm-Up.docx).

They should be starting to make the connection between the mathematical processes used to solve these two problems. When they work on these two problems I ask them:

• How do these two problems relate to each other?

Problem (2) is a challenge when it comes to think about how the two negative signs affect the graph. I ask students these questions:

• Do the two negative signs cancel each other out? Why or why not?
• Do the two negative signs have the same affect on the graph of the function? Why or why not?
• How do you choose inputs for this function?

Though it seems simple, asking students these questions helps them understand some of the complexity involved in these transformations. Eventually, they should be able to link these changes to the function to reflections over the x- and y-axes. Hopefully they can articulate this today.