arrow_back Back to Functions

Functions: Probing Questions

Whether you are looking for a question to stimulate discussion in lesson, or a challenge at the end of a homework, then hopefully you will find these useful.

Contents

Convince Me That... keyboard_arrow_up

Back to Top

I use Convince Me That questions lots in my lessons and homeworks. Providing students with a statement and challenging them to come up with as many different ways of convincing you as possible can lead to some fascinating discussions. The different ways of seeing the same thing can also help improve the depth of students’ understanding. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!

There is a graphically relationship between a function and its inverse

The inverse function of $f\left(x\right)=2x+1$  is  $f^{-1}\left(x\right)=\frac{x-1}{2}$

If f(x) = x + 5, f(2x) is not 2x + 10

If f(x) = x + 1, and g(x) = x², then fg(3) has a smaller value than gf(3)

If f(x) = x + 4 and g(x) = x – 5 then gf(x) and fg(x) are the same.

If f(x) = 2x  and g(x) = x – 5 then fg(x) and gf(x) are not the same.

VI3 Treatment keyboard_arrow_up

Back to Top

We devised VI3 Treatment as a versatile way of giving students meaningful follow-up work at once we have marked their homework. The idea is that students are challenged to come up with 3 things with certain constraints. These are ideal to use as an extension for students who have got everything correct, and also as further purposeful practise for students who have got a particular question wrong. Use the ideas below and adapt them accordingly, using different numbers where appropriate. Either mark them yourself or better still, get other students to do it. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!

Write down 3 different functions for f(x) so that f(-3) = 5

Write down 3 functions that are "self inverse" i.e. the function and inverse are the same

Write down 3 different functions whose function and inverse give the same answer when you substitute 4 into them

Write down 3 different functions for f(x) and g(x) so that fg(x) and gf(x) are the same