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#### Transforming Graphs and 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*
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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 studentsâ€™ 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!

y = f(x) + 2 is a translation of y = f(x) 2 places up

y = f(x + 3) is a translation of y = f(x) 3 places to the left, not the right

y=f(-x) is a reflection of y = f(x) in the x-axis

We can use the completed the square form of quadratic expressions, together with our knowledge of transformations, to find the minimum point of the curve

It doesn't matter what order we do two translations, but it does matter what order we do a reflection and a translation

#### VI3 Treatment *keyboard_arrow_up*
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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 idea 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. 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!

The point (3, -2) lies on the graph of y =
f(x). Write down the new co-ordinates of the point on:

1) y = f(x) + 5

2) y = f(x + 3)

3) y = -f(x)

Carry out 3 successive transformations on the graph of y = f(x), writing down where the point (-4, 7) goes each time