Questions: Select the correct answer. Consider function f. f(x) = √(x-2) Which graph represents function f? A. W B. X C. Y D. z

Transcript text: Select the correct answer. Consider function $f$. \[ f(x)=\sqrt{x-2} \] Which graph represents function $f$ ? A. W B. X C. $Y$ D. $z$

Solution

Solution Steps

Step 1: Identify the Domain of the Function

The function given is $ f(x) = \sqrt{x - 2} $. The expression inside the square root must be non-negative for the function to be real-valued. Therefore, $ x - 2 \geq 0 $, which simplifies to $ x \geq 2 $.

Step 2: Determine the Starting Point

Since $ x \geq 2 $, the function starts at $ x = 2 $. At $ x = 2 $, $ f(2) = \sqrt{2 - 2} = \sqrt{0} = 0 $. So, the point (2, 0) is on the graph.

Step 3: Analyze the Shape of the Graph

The function $ f(x) = \sqrt{x - 2} $ is a square root function shifted 2 units to the right. The graph will start at (2, 0) and increase slowly as $ x $ increases.