The graph starts at around x = 0. At x = 0, the graph's y-value is 2. There are no x-values that are less than 0.
The graph crosses the following points: (1,1); (4,0); (9, -1)
The distance between each y-value is exponentially increasing, as the slope of the graph is slowly decreasing as x approaches infinity.
Based on this information, we can say that this graph is a transformation of the base function,
y = √x
To determine the transformations made, we need to compare the graph to the original base function (attached below).
The basic function starts at 0, and has a positive slope. It reaches the points (1,1); (4,2); and (9,3).
The graph in the question shows the function start at 2, and the negative slope reaching the points mentioned earlier in the answer.
Based on this information, we can conclude that
y = -√x + 2.
