The fuction I choose on this graph is the absolute value fuction, which is y=x draw in black, after this I can do Transformation to the function which is changing it from the orginal. To graph the reflection of y=x multiply by (-1), you get y=-x draw in purple above. After the vertical translation, shift 5 units up, it can be written as y=x+5; in the graph above the whole thing move up in the vertical line-the coordinates for the y-axis is 5. For horizontal translation it was also shifting 5 units, but not on the vertical line but on the horizontal line-the coordinates for the x-axis is 5,because y=x-5 it has a subtract sign inside so we move it 5 units to the right from 0. Combining horizontal and vertical translation it can be written as y=x-5+5 ,the +5 was outside so we shift up on the vertical line then right 5 units because there is the -5 inside. To graph the reflection of the function after the horizontal and vertical translation you have only have to multiply the whole thing with (-1) then you get y=-x-5-5.