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
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