Education Technology

Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Functions

Families of Functions

Activity Overview


This lesson involves changing the sliders for a, h and k on each page and observing the effects each has on the graphs of the functions. Students will fill in the table on the student activity sheet as they investigate the effects of parameters a, h and k on each graph. Students will use the completed table to make generalizations about the effects of a, h and k on the graphs of any function. As a result, students will:
  • Describe the transformations to a parent function using their generalizations.


  • Students will investigate the effects parameters a, h, and k have on a given function.
  • Students will generalize the effects that parameters a, h, and k have on any function.


  • Function
  • Parameter
  • Vertical stretch
  • Vertical compression
  • Horizontal translation
  • Vertical translation
  • Transformation
  • Scale factor