Question

the image shows the graph of the parent function. which function from shifting the parent function 3 units down and 1 unit to the
y = \sqrt{x - 1} - 3
y = \sqrt{x + 1} - 3
y = \sqrt3{x - 1} - 3
y = \sqrt3{x +

Explanation:

Step1: Identify parent function

The graph matches $y=\sqrt{x}$ (square root function, defined for $x\geq0$, increasing, starts at origin).

Step2: Apply horizontal shift right 1 unit

For horizontal shift right $h$ units: replace $x$ with $x-h$. Here $h=1$, so $y=\sqrt{x-1}$.

Step3: Apply vertical shift down 3 units

For vertical shift down $k$ units: subtract $k$ from the function. Here $k=3$, so $y=\sqrt{x-1}-3$.

Answer:

$y=\sqrt{x-1}-3$ (the green option)