What does swapping x for x- 2 do to the graph? It might help to graph y= x- 2 itself first.
Same for swapping x for -x.
What does swapping y for y+ 5 do to the graph? What is the difference between y= x and y= x- 5?
the transformation f(x+2) translates the graph 2 points on the left. The transformation -f(x+2) -5 translates the function 2 points to the left and 5 points down then refleccts it over the x-axis.
The transformation f(-x) +5 reflects the graph over the y-axis and translates it up 5 points.
MINOAS