Ch. P Graphing Functions by Thanh Quotient

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= |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.