What we are trying to do here is to show the different transformations of a function
The function that I use is y=| x |, this function is to show how the graph will look like when x is an absolute value and it will show what kind of answer will you get when you plug in x.
1. The original function is in Yellow, showing you were did I began at.
2. Then we transform the original function into a Vertical Translation, which is stated in penish color and the equation is y=abs(x)+1. ( y=| x |+1 ). In a vertical translation you could determined how many space to move on the Y-axis by positive or negative integers.
3.From Vertical Translation we went back to the original function graph and move to the right and formed Horizontal Translation and the equation is y=abs(x-2). ( y=| x -2| ). You could see that in pink. For horizontal translation you could determine whether you should move right or left is by looking at what "x" is doing. If "x" is subtracting then you will move to the right on the x-axis, and left if you are adding.
4.The next one is going to be hard to see because it is in orange and that one is the Combing Vertical and Horizontal Translation. The function is y=abs(x-5)+2. ( y=| x- 5 |+2 ). From the explanation above of Vertical Translation and the Horizontal Translation, all you need to do is to combing the directions and you will have your combination of the vertical and horizontal translation.
5. This one is a Reflection over the x-axis the color is in light blue the equation for this one is y=-[abs(x)]. ( y= -| x | ). Basically you are just opposing the original function.
6. There are also a Horizontal Reflection, the color is yellow and you can use barely see it but it is there. The equation for this one is y = abs(x). ( y= | x |). So now you could understand why is the line is kind of limeish color because it is a mixture of green and yellow and it is basically the same line.
7. The last one is a Combing Translations and Reflection. It is in the color of dark green, the equation for this one is y= -abs(x-5)+2. ( y= -| x - 5|+ 2). It is similar to the horizontal and vertical translation except you are putting them in a opposing side of the original.
From all of that is the explanation of the color and what I did, I didn't explain about the red one, because that is just a reflection of the vertical translation.