1. The original graph i used is the one in color "Black" . It's original funtion is y= [x] (y is equal to the absolute value of X. That is what you get if you were to graph it.
2. I wanted to verticle translate this original graph so what i do is i move it down vertically 4 units. This vertical translation gave us the new funtion y=[x] -4 which is shown is the red graph above.
3. Then, Said i want make a horizontal translation it's very similar to verticle translation but this time you would have to go horizontally across the x-intercept instead. In blue graph above i horizontal translate it 8 units to the left which gave me the new function of y= [x-8]
4. Now if you want to recflect this across the x-axis you would have to do the reflection by flipping the graph over (shown in purple graph above). This new funtion is y= -[x] (where negative is on the outside)
5. After that, you can also combine both the vertical "and" horizontal translation. This means that you are moving the graph in 2 directions, "vertically" and "horizontally". In this funtion i move the graph 8 units to the right" horizontally" and 4 units down "vertically". It's shown in the green graph above.
6. Finally, WHAT'S Awesome! is that you can actually combine the whole thing by creating this tranformation just by putting together the ( verical (4 down) +horizonal (8 right) translation and our reflection across the x-axis) When you put them together your result will be the same as in my green graph. This new funtion gives us y= -[x-8]-4