For chapter P, we did our project on graphing parent Functions. We had to perform Transformations: both Vertical and Horizontal Translations, and Reflections across the X-axis and the Y-axis. One of the parent functions i graphed was the absolute value parent function (the picture on bottom left of the first picture). The original parent function was

Y=

Y=

Y=

**|**x**|**. I first did a vertical translation by moving the graph up by one unit and adding 1 to the function outside of the absolute value sign:Y=

**|**x**| +**1, next i did a horizontal translation by moving the graph one unit to the right and subtracting a 1 from the x inside of the absolute value sign: Y=**|**x**-**1**|**, I then combined these two vertical and horizontal translations and moved the graph up one unit and one unit to the right giving the equation Y=**|**x**-**1**| +**1. Then i did a reflection across the Y-axis (also known as a horizontal reflection) which did not change anything except for the equation of the parent function which turned the "X" inside of the absolute value to negative giving us Y=**|**-x**|**and i also did a reflection across the X-axis (also known as a vertical reflection) which flipped the graph upside down below the x-axis, this changed the absolute value parent function into Y=**-|**x**|**, where the negative is outside the parent function. Finally i did a vertical and horizontal translation with a vertical reflection where i moved the original parent function one unit up and to the right flipped upside down below the x-axis before i perform the translations, giving me Y=**-|**x**-**1**|**- 1.
## 2 comments:

Hi Thanh,

Please correct

Y= |x|, where Y=X.

Does Y = X?

Great Job Thanh!

20 points

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