Step-by-step explanation:
Domain:
The expression inside the square root, (x - 1), must be non-negative.
So, x - 1 ≥ 0.
Solving for x, we get x ≥ 1.
Therefore, the domain is x ≥ 1, or in interval notation, [1, ∞).
Range:
The square root function, √(x - 1), always outputs non-negative values (or zero).
However, in this case, we have a negative sign in front of the square root, which flips the output to be non-positive values (or zero).
Then, we add 5 to the negative square root, which shifts the graph upward by 5 units.
This means the range will be all values less than or equal to 5.
Therefore, the range is y ≤ 5, or in interval notation, (-∞, 5].
