Question

given the function f(x)=sqrtx, which of the following functions represents the transformation of f(x) that is shifted right 6 units, up 3 units, stretched vertically by a factor of 2, and reflected across the x axis

Answer 1

Apply the horizontal shift inside, then the vertical stretch+reflection, then the vertical shift. Starting from f(x)=√x:

1. Right 6: √(x−6)
2. Stretch by 2 and reflect across x-axis: −2√(x−6)
3. Up 3: −2√(x−6) + 3

So the transformed function is g(x) = −2√(x−6) + 3.
Domain: x ≥ 6. Range: (−∞, 3].

(If the “up 3” were applied before the reflection/stretch, the result would be −2(√(x−6)+3) = −2√(x−6)−6, but the standard order is as given above.)