To determine the domain and range of the function $y = \sqrt{2x - 10}$, we need to focus on the conditions that must hold for the square root to be defined and for the output values of $y$.

Step 1: Domain

The domain of a square root function is restricted because the expression inside the square root must be greater than or equal to zero (you cannot take the square root of a negative number in the real number system).

So, we solve for:

$2x - 10 \geq 0$

$2x \geq 10$

$x \geq 5$

Thus, the domain is $x \geq 5$, meaning that $x$ can take any value greater than or equal to 5.

Step 2: Range

The square root function produces only non-negative values, so the range is restricted to values of $y$ that are greater than or equal to zero.

Additionally, when $x = 5$, $y = \sqrt{2(5) - 10} = \sqrt{0} = 0$. As $x$ increases, $y$ increases because the expression under the square root becomes larger.

Thus, the range is $y \geq 0$.

Conclusion:

• The domain is $x \geq 5$
• The range is $y \geq 0$

So, the correct answer is: B.) Domain: $x \geq 5$, Range: $y \geq 0$

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Would you like more details on how square root functions behave, or have any questions about this problem?

Here are some related questions:

1. How do we find the domain and range of rational functions?
2. What are the characteristics of the graph of a square root function?
3. How do transformations (shifts, stretches) affect the domain and range of a square root function?
4. What is the domain and range of the function $y = \sqrt{x+3} - 4$?
5. Can a square root function have a negative range?

Tip: Always ensure the expression inside a square root is non-negative when determining the domain of the function.