Chapter P: Graphing Functions

1. First, I chose the function y=lxl and would represent our "start" or original function. This is shown in BLACK.
2. Next, I performed a vertical translation. The function would be y=lxl-3, where you go 3 units down from the original function. This is shown in RED.
3. Then, I performed a horizontal translation. The function would be y=lx+4l, where you move 4 units to the left of the original function. This is shown in BLUE.
4. After, I combined both the vertical and horizontal translation, and transformed the original function into y=lx+4l-3 where the graph moved 4 units to the left of the x-axis then 3 units down the y-axis. This is shown in GREEN.
5. Then, I performed a reflection where the original function would be flipped 180 degrees (over x-axis) This is shown in PURPLE.
6. Finally, I made a transformation by combining step 4 and 5. This made the function y=-lx+4l-3 where the original function was reflected over the x-axis and moved 4 units to the left of the x-axis and 3 units down the y-axis from the original function. This is shown in BLACK.