We need to find the following operation
[tex]T_{(-1,2)}\circ R_{x-axis}(QRST)[/tex]which means that we need to find first the reflection over the x-axis of the figure QRST:
[tex]R_{x-axis}(QRST)[/tex]and then translate the result 1 unit left and 2 units up:
[tex]T_{(-1,2)}[/tex]In this regard, the rule for a reflection over the x-axis is given by
[tex](x,y)\longrightarrow(x,-y)[/tex]Then, by applying the reflection rule, we have that
[tex]\begin{gathered} Q(1,3)\longrightarrow Q^{\prime}(1,-3) \\ R(3,-3)\longrightarrow R^{\prime}(3,3) \\ S(0,-2)\longrightarrow S^{\prime}(0,2) \\ T(-2,1)\longrightarrow T^{\prime}(-2,-1) \end{gathered}[/tex]Now, the translation rule for 1 units to the left and 2 units up
[tex](x,y)\longrightarrow(x-1,\text{ y+2)}[/tex]Then, by applyin this rule to the last result, we have
[tex]Q^{\prime}(1,-3)\longrightarrow Q´´(1-1,-3+2)=Q´´(0,-1)[/tex]and
[tex]R^{\prime}(3,3)\longrightarrow R´´(3-1,3+2)=R´´(2,5)[/tex]and
[tex]S^{\prime}(0,2)\longrightarrow S´´(0-1,2+2)=S´´^{}(-1,4)[/tex]and finally,
[tex]T^{\prime}(-2,-1)\longrightarrow T´´^{}(-2-1,-1+2)=T´´(-3,1)[/tex]Therefore, the answer is:
[tex]\begin{gathered} Q´´(0,-1) \\ R´´(2,5) \\ S´´^{}(-1,4) \\ T´´(-3,1) \end{gathered}[/tex]