You may like to share one or two pieces of this sample student work during the task to help prompt discussion and encourage students to reflect on different ways to complete the table. To give you more flexibility in how you use the sample work, there is an extra printable copy without questions.

Group A

What does it mean for a curve to be increasing for \(x>1\)? Try to draw a sketch to show this.

What do the other headings mean?

What do you think these students did to work out these headings?

Group B

Do the functions in this table have the properties identified in their row and column?

How do you think these students constructed their functions in the top and middle rows?

Could you modify any of the functions in the table to complete the table in a different way?

Group C

Can you follow these studentsâ€™ method for finding their example functions?

How could you modify the examples or row and column headings so that they are consistent with each other?

Group D

If a function has stationary points where \(x=0\) and where \(x=-3\), could you suggest what its gradient function might be?

How can you check whether the suggested functions have the required properties for their row and column?

Are there any functions already in the table which you could modify to help you complete the table?

Group E

These students have used quadratics in several cells. How can you modify these to complete the table?

Could you use the same function in more than one cell?