Starter

Combining transformations domino trail.

5 Questions

A translation of 5 units in the x direction means that you replace…

f(x)-5 represents what transformation?

y=(2x)2 represents what transformation of y=x2

What two transformations change y=3x+1 into y=-3x+2?

Why must you be careful if translating and stretching in the x direction?

x with x-5

Translation 5 units down in y or -5 units in y

Stretch scale factor 1/2 in the x direction

Reflect in the x axis followed by translation of 1 unit in y

The order matters and gives a different image.

Combining Transformations

Aims: To be able to find the result of two transformations where the same variable is replaced twice.

Learning Outcomes

• Name: What are combined transformations of functions?

• Describe: How to perform a combination of transformations where the same variable is replaced.

• Explain: How to show these combinations of transformations in function notation. How you can tell find out what pairs of transformations cause a function to change into another.

Double Replacements

• If we replace x and y in each combination of transformations.

• This means that the order does not matter!• If you do two different transformations that replace the

same value you must be careful of the order.

2 4 6

–2

2

4

x

y

2 4 6

–2

2

4

x

y

Translate Stretch Stretch Translate

Double Replacement

• This can be explained by algebra you replace the x (and only the x) with the required replacement to complete each transformation in the correct order.

333

333

3

))2(3()3(

0

2 Translate then anddirection in the

3

1 sfStretch

)2)3(()2(

direction in the 3

1 sfStretch then and

0

2 Translate

then... Take

xxx

x

xxx

x

xy

1 minute

Example

image. theofequation

thefind 3-

0slated then tranand axis the

in reflected is 2equation The 3

x

xxy

1 minute

and another

image. theofequation

thefind 2

0slated then trananddirection the

in 3 sf stretched is 5

2equation The

2

y

x

xy

Relay

Have a go at relay questions in pairs

5 questions

Exam Questions

Most exam questions on this topic include trig functions (a lot on inverse trig functions).

We will be revisiting this in 3 weeks.

Learning Outcomes

• Name: What are combined transformations of functions?

• Describe: How to perform a combination of transformations where the same variable is replaced.

• Explain: How to show these combinations of transformations in function notation. How you can tell find out what pairs of transformations cause a function to change into another.

Learning Outcomes

• Name: Combined transformations are where you perform two transformations on a function.

• Describe: Just as with single transformations you must replace the variable as required to make the transformation (see last lesson). When replacing it is important that just the variable is replaced with brackets around the replacement.

• Explain: The function notation follows the same replacements as equations if you think of it as y=f(x). You look at the changes to variables x and y (changes in y effect every term on the other side and changes to x only change x; this is true if it is y=…)

Multi Guess

Have a go at the multiple choice questions on the sheet on the sheet

Once finished start the exercise and complete for homework. Solutions are on moodle.

Homework

Edpuzzle

2 videos on modulus function

and

Complete exercise on worksheet.