Ch1 Real Life Function project

I did my chapter 1 project on New Moon stars and their birth cities. The independent variables are Stars' names. The dependent variables are the stars' birth cities. The domains are: {Kristen Stewart, Robert Pattinson, Taylor Lautner, Ashley Greene, Peter Facinelli, Elizabeth Reaser, Kellan Lutz, Nikki Reed, Jackson Rathbone}. And the ranges are: { Los Angeles, London, Grand Rapids, Jacksonville, Queens, Bloomfield, Dickenson, West Los Angeles, Singapore}.

Graphing Functions

I used y=x^2 (black) as my graphing function and its vertex is located on the 0 of the y-axis and 0 on x-axis, which is the origin. The first transformation I performed was the vertical translation (red). To perform the vertical translation, all I did was to add 3 to my original graphing function, which makes it y=x^2+3 and on my graph, I only have to move the graphing function 3 units up. Next, I made a horizontal translation (blue). Since I moved the function 4 units to the left, my new function is y=(x+4)^2. In horizontal translations, you do the opposite of the other, which means that if its negative, you move to the right and you move positive to the left. After performing the vertical translation and the horizontal translation, I now somewhat combine them and turn them into something called a vertical horizontal translation(green). So I moved the function 3 units up and 4 units left and new function would be y=(x+4)^2+3. Then I made a vertical reflection (purple) across x-axis. To make a vertical reflection, all I did was to multiply the graphing function by negative and my new function would be y=-x^2. Lastly, I performed a vertical horizontal reflection (black). Like the vertical horizontal translation (green) I did, now I just have to multiply it negative and voila, there is my new vertical horizontal reflection y=-(x+4)^2-3.