Question

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Explanation:

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Step1: Identify parent & transformations

Parent: $y=\sqrt{x}$. Endpoint $(0,0)\to(0,0)$? No, graph crosses $(1,1)$, $(4,2)$ shifted up? No, passes $(0,0)$, $(1,2)$, $(4,4)$. Vertical stretch by 2.

Step2: Write final equation

$y=2\sqrt{x}$

Step1: Identify endpoint shift

Parent endpoint $(0,0)\to(-2,-8)$: left 2, down 8.

Step2: Identify stretch

Point $x=2$: $y=\sqrt{2+2}-8=2-8=-6$, matches graph. Stretch factor 1.

Step3: Write equation

$y=\sqrt{x+2}-8$

Step1: Identify reflection & shift

Parent reflected over x-axis, endpoint $(0,0)\to(0,0)$? No, endpoint $(8,-4)$, left 0, down 0? No, $y=-\sqrt{8-x}$: when $x=0$, $y=-\sqrt{8}\approx-2.83$ no. Wait, endpoint $(8,-4)$, $x=0$: $y=0$. So $y=-\sqrt{8-x}$ no, $y=-\sqrt{-x+8}$: $x=8,y=0$; $x=0,y=-\sqrt{8}\approx-2.83$ no. Wait, $y=-\frac{1}{2}\sqrt{-x+8}$: $x=8,y=0$; $x=0,y=-\frac{1}{2}\sqrt{8}\approx-1.41$ no. Wait, graph has endpoint $(8,-4)$, $x=-1$: $y=0$. So $y=-\sqrt{-x-1}+0$? No, $x=-1,y=0$; $x=8,y=-\sqrt{-9}$ invalid. Correct: $y=-\sqrt{8-x}$ is wrong. Wait, right reflection over y-axis, shift right 8, down 0, vertical stretch 1, reflect x-axis: $y=-\sqrt{8-x}$.

Answer:

$y=2\sqrt{x}$

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