Looking at complex functions can be scary, but understanding where they come from and how they relate to each other can help!
Using common parent functions, students will practice function transformations, specifically shifting, by both graphing and writing equations. The concept of a "family tree" is used to show students that functions can be related, but also unique individuals.
Given a graph of the original function, students will draw four "family members" or transformations: shift up, shift down, shift left, and shift right. Once they sketch their new "family members," Students must write the corresponding equations for their functions.
Students create their own family of functions for six common graphs in this packet:
y = x
y = sqrt(x)
y = I x I
y = 1/x
y = x^2
y = x^3
You could use this packet as an in-class assessment, take-home practice, exit ticket, or group project.