Graphing Functions / Transformations

1) First, I graphed the Absolute Value parent function.
y = "Absolute Value of X"

2) Then, I did a vertical translation in the color red. I translated the parent function 10 units up along the y-axis and got the new graph,
y = "The Absolute Value of X" plus 10

3) Next, I did a horizontal translation in the color blue. I translated the parent function 6 units to the left along the x-axis and got the new graph,
y = "The Absolute Value of X plus 6"

4) I already did a vertical and a horizontal translation, now I did a vertical and horizontal translation combined in the color green. First, I translated the parent function 10 units to the right and 2 units up, and got the new graph,
y = "Absolute Value of X minus 10" plus 2


5) Next, I did a reflection over the x-axis in the color purple. All I did was flipped the Absolute Value parent function upside down, to get the new graph,
y = - "Absolute Value of X"

6) Lastly, I combined a reflection, vertical translation, and horizontal translation in the color black. First, I translated the graph 10 units to the right, 2 units up, and then reflected the graph over the x-axis to get the final graph,
y = - "Absolute Value of X minus 10" plus 2

Altogether, I did five transformations.