The mapping given is a composition, we know that if we make a reflection across the y-axis we have that:
[tex](x,y)\rightarrow(-x,y)[/tex]
We also know that a vertical translation is given by:
[tex](x,y)\rightarrow(x,y+b)[/tex]
Now, in this case, if we first perform the reflection and then the translation four units up we will have the mapping:
[tex](x,y)\rightarrow(-x,y+4)[/tex]
Therefore, the mapping is given as:
[tex](T_{0,4}\circ r_{y-axis})(x,y)\rightarrow(-x,y+4)[/tex]
