Question: The graph of y = sqrtx is given below: Find a formula for each of the transformations whose graphs are given below. Recall that square root is entered as sqrt. a) y = b) The first graph is a square-root curve starting at the origin and increasing to the right, labeled top-left. The graph in a) is a reflected square-root curve starting at the origin and decreasing to the right, labeled center. The graph in b) is a reflected square-root curve with endpoint at the origin extending to the left and above the x-axis, labeled center.

1. **Problem Statement:** We start with the basic square root function: $$y = \sqrt{x}$$ We are asked to find formulas for the transformations shown in the graphs: a) A reflected square-root curve starting at the origin and decreasing to the right. b) A reflected square-root curve with endpoint at the origin extending to the left and above the x-axis. --- 2. **Recall the basic transformation rules for square root functions:** - Reflection about the x-axis: multiply the function by $-1$, so $y = -\sqrt{x}$. - Reflection about the y-axis: replace $x$ by $-x$, so $y = \sqrt{-x}$. --- 3. **Analyze graph a):** - The curve starts at the origin $(0,0)$. - It decreases to the right, which means it is reflected about the x-axis. Thus, the formula is: $$y = -\sqrt{x}$$ --- 4. **Analyze graph b):** - The curve is reflected about the y-axis (extends to the left). - It is also reflected about the x-axis (above the x-axis but decreasing to the left). This means the function is reflected about both axes: $$y = -\sqrt{-x}$$ --- **Final answers:** a) $$y = -\sqrt{x}$$ b) $$y = -\sqrt{-x}$$