graphing a radical function\nthe domain of $y = \\sqrt{x - 5}-1$ is\nthe range of $y = \\sqrt{x - 5}-1$…

Explanation:

Step1: Find the domain

For the square - root function $y = \sqrt{x - 5}-1$, the expression inside the square - root must be non - negative. So we set $x−5\geq0$. $x−5\geq0\Rightarrow x\geq5$.

Step2: Find the range

The square - root function $\sqrt{x - 5}\geq0$. Then $y=\sqrt{x - 5}-1\geq - 1$.

Step3: Analyze the graph

The function $y = \sqrt{x - 5}-1$ is a square - root function that is shifted 5 units to the right and 1 unit down from the parent function $y=\sqrt{x}$. The starting point of the graph is at $(5, - 1)$ and it increases as $x$ increases.

Answer:

The domain of $y=\sqrt{x - 5}-1$ is $[5,\infty)$. The range of $y=\sqrt{x - 5}-1$ is $[-1,\infty)$. (Without specific graph labels to choose from in the dropdown, we can't fully answer the third part. But conceptually, the graph starts at the point $(5, - 1)$ and curves upwards as $x$ increases.)