Question

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Explanation:

Identify the function and its transformations

Using the Square Root Function Transformations, Horizontal Translation, and Vertical Translation knowledge points

$$
LATEXBLOCK0
$$

Determine the domain of the function

To find the domain, the expression inside the square root must be non-negative:

$$
LATEXBLOCK1
$$

Determine the range of the function

Since the principal square root is always non-negative (\(\sqrt{x-7} \ge 0\)):

$$
LATEXBLOCK2
$$

Answer:

For the function \(y = \sqrt{x - 7} + 1\):

The domain is \(x \ge\) <blank>7</blank>
The range is \(y \ge\) <blank>1</blank>