find the domain and range of the function $y = \\sqrt{x - 3}+6$.\na domain: $x\\geq0$; range: $y\\geq0$\nb…

find the domain and range of the function $y = \\sqrt{x - 3}+6$.\na domain: $x\\geq0$; range: $y\\geq0$\nb domain: $x\\geq - 3$; range: $y\\geq - 6$\nc domain: $x\\geq0$; range: $y\\geq6$\nd domain: $x\\geq3$; range: $y\\geq6$

find the domain and range of the function $y = \\sqrt{x - 3}+6$.\na domain: $x\\geq0$; range: $y\\geq0$\nb domain: $x\\geq - 3$; range: $y\\geq - 6$\nc domain: $x\\geq0$; range: $y\\geq6$\nd domain: $x\\geq3$; range: $y\\geq6$

Answer

Explanation:

Step1: Find the domain

For the square - root function to be well - defined, the expression inside the square root must be non - negative. So we set $x - 3\geq0$. $x-3\geq0\Rightarrow x\geq3$

Step2: Find the range

The square - root function $\sqrt{x - 3}\geq0$. Then $y=\sqrt{x - 3}+6$. Since $\sqrt{x - 3}\geq0$, we have $y=\sqrt{x - 3}+6\geq0 + 6$. $y\geq6$

Answer:

D. domain: $x\geq3$; range: $y\geq6$