The graph looks like an absolute function.
If we were to compare the function
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!