Teaching Group Year 9 Autumn Term
Resources
VTB worksheets, excel resources
Aspects of National Curriculum Frame Work to be covered.
Finding the inverse of a linear function. Pg 161-163
Lesson context/focus:
Focus is on understanding the meaning of an inverse function and how to work them out.
Key words : linear, inverse, function
Misconceptions
Pupil’s must remember that when doing the inverse of a function they must do the inverse of all the functions in that and not just part of it.
Learning Objectives:
To be able to find the inverse of a linear function.

Structure of lesson
Starter : Explain that a function is an order of events and that in an equation putting a value in and performing the function will result in an answer. For example
3  multiply by 2  add 5  11
By doing this function of multiplying and then adding a result is produced.
Whenever we solve equations we are in fact doing this process although we may not write it in this manner.
To practice algebraic manipulation try the Linear equations (XP). (15mins)
Main : Hand out worksheet Ma36B004 Qu 1-12. This allows the students to practice writing out what the functions are which is important for understanding inverse functions. (10 mins)
In the starter example we can write this function mathematically instead of in words. x is the value we put in and it maps onto another value once we have performed the function.
3  (3  2) + 5  11
If our value was not 3 but any value we would write it as x  3  x + 5 x  3x + 5
So in this case x maps to 3x + 5
On worksheet Ma35D001 Qu 1 ask the children to work out the outputs.
(10mins)
Qu2 on this worksheet is about inverse functions and if we use our example from the starter which was x  3x + 5 we need to create a function that takes us back to the original e.g 3x + 5  x
In this case we need to minus 5 and then divide by 3.

Therefore the inverse function of 3x + 5  x is………x  x – 5
3
Ask the pupils to complete question 2 of the worksheet. (20mins)
Extension :
On worksheet Ma35D001 Qu 2 the more able pupils could draw the graphs of some of the functions and also the inverse functions to see the symmetrical nature of the lines.
Homework : Continue with worksheet Ma34D006 questions 4 –7.