The parent function of the original graph is

*f*(x)=x (as indicated with the light pencil).The first transformation of the graph would be a vertical transformation by moving the original graph of

*f*(x)=x down 5 units, transforming the graph to*f*(x)=x-5 (as indicated with the red graph).The next transformation of the graph would be a horizontal transformation by moving the original graph of

*f*(x)=x to the left 2 units, transforming the graph to*f*(x)=x+2 (as indicated with the blue graph).The next transformation of the graph would be a horizontal-vertical transformation by moving the original graph of

*f*(x)=x to the left 2 units and down 4 units, transforming the graph to*f*(x)=x+2-4 (as indicated by the green graph).The next transformation of the graph would be a reflection. To reflect across the x-axis, you have to multiply the original graph by (-1). Thus the new graph,

*f*(x)=-x (as indicated by the purple graph).The final transformation of the graph would be a horizontal-vertical reflection. The graph would be moved 2 units to the left, 8 units up, and the whole function would be multiplied by (-1),

**(as indicated by the black graph).***f*(x)=-x+2+8
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