<p>The range of the function \(\sqrt{x-5}\) is \([z, \infty)\), where \(z\) is __________.</p>
Step-by-Step Solution
Key Concept: The range of a square root function √(x-a) starts at 0 (the minimum value of the square root) and extends to infinity. The parameter z represents this minimum value, which occurs when the argument equals zero.
<p><strong>Step 1:</strong> Identify the domain constraint. For √(x-5) to be defined, we need x - 5 ≥ 0, which gives x ≥ 5.</p><p><strong>Step 2:</strong> Find the range by determining all possible output values. When x = 5 (minimum domain value), we get √(5-5) = √0 = 0.</p><p><strong>Step 3:</strong> As x increases from 5 to ∞, the expression (x-5) increases from 0 to ∞, so √(x-5) increases from 0 to ∞.</p><p><strong>Step 4:</strong> Therefore, the range is [0, ∞), which means z = 0.</p><p>∴ Answer: <strong>0</strong></p>
Correct Answer: 0