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**.

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