Answer:
y = -3√(x -1) +2
Explanation:
You want the equation of the translated, reflected, and scaled square root function in the given graph.
Translation
We can find the amount of translation by looking at the position of the point that corresponds to (0, 0) on the graph of the parent function. That end point where the slope is vertical is located at (1, 2) on the given graph.
When a function y = f(x) is translated by (h, k), it becomes ...
y = f(x -h) +k
For (h, k) = (1, 2) the translated function is ...
y = f(x -1) +2 = √(x -1) +2
Scale factor
When the function is scaled, its value is multiplied by the scale factor. If that factor is 'a', our scaled and translated function is ...
y = a√(x -1) +2
To find the scale factor, we can use the second point on the curve: (2, -1). Using these values for x and y gives ...
-1 = a√(2 -1) +2
-3 = a . . . . . . . . . . subtract 2, simplify
The transformed function is ...
y = -3√(x -1) +2
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Additional comment
The function is scaled before it is translated, so the scale factor does not apply to the translation.
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