The graph looks like an absolute function.
If we were to compare the function [tex]y= |x|[/tex] to this graph (see image attached), we see that the function in the graph has only shifted two to the right.
To write in function form, when shifting the graph horizontally
- add within the function --> move the graph to the left
- subtract from within function --> move the graph to the right
In this case, since we want to shift over two spots horizontally, we get the function is
y = |x -2|
Now we want to find the function that is increasing and decreasing over the same interval.
The only function that looks the most similar is y = 4|x-2|.
The reason for that is because the y = 4|x-2| is just a stretched version of y= |x-2| meaning the point where it is increasing or decreasing should stay the same. Look at the second image I attached.
Hope it helps!
