1. The problem asks us to find the equation of a function whose graph is a transformed square-root curve. 2. The basic square-root function is given by $$y=\sqrt{x}$$. 3. The graph starts at about (0, 5.5) and decreases as x increases, passing near (10, 3). 4. This suggests a vertical shift and a reflection because the basic square-root function increases, but this one decreases. 5. A general transformation of the square-root function can be written as $$y = a\sqrt{x} + b$$ where $a$ controls vertical stretch and reflection, and $b$ controls vertical shift. 6. Since the graph decreases, $a$ is negative. 7. At $x=0$, $y=5.5$, so substituting gives $$5.5 = a\sqrt{0} + b = b$$, so $b=5.5$. 8. At $x=10$, $y=3$, so substituting gives $$3 = a\sqrt{10} + 5.5$$. 9. Solving for $a$: $$a\sqrt{10} = 3 - 5.5 = -2.5$$ $$a = \frac{-2.5}{\sqrt{10}}$$ 10. Therefore, the equation is $$y = -\frac{2.5}{\sqrt{10}}\sqrt{x} + 5.5$$.