Combined Transformation (Part 2)

Now let's look at what happens outside the bracket (which applies to y)

We had

from the previous part and eventually we want to arrive at

Vertical Translation of 2 units downwards 2.

Vertical stretching of scale factor 2 vertically

Vertical Stretching of scale factor 2 vertically 2.

Vertical translation of 2 units downwards.

Finally, can you sketch the final graph of

You can check your answer using the applet which uses

below.

Alternatively, you can try using the formula

. Note: the order of transformation is different from the above when using