Question

All i need to know is the type of mapping

Answer 1

The mapping given is a composition, we know that if we make a reflection across the y-axis we have that:

`(x,y)\rightarrow(-x,y)`

We also know that a vertical translation is given by:

`(x,y)\rightarrow(x,y+b)`

Now, in this case, if we first perform the reflection and then the translation four units up we will have the mapping:

`(x,y)\rightarrow(-x,y+4)`

Therefore, the mapping is given as:

`(T_(0,4)\circ r_(y-axis))(x,y)\rightarrow(-x,y+4)`