Question

which equation describes the graph? y = √x - 2 y = √x - 2 y = √x + 2 y = √x + 2

Explanation:

Step1: Analyze domain of square - root functions

For a function $y = \sqrt{u}$, the expression under the square - root $u\geq0$.

Step2: Analyze $y=\sqrt{x - 2}$

The domain is $x-2\geq0$, i.e., $x\geq2$. When $x = 2$, $y = 0$.

Step3: Analyze $y=\sqrt{x+2}$

The domain is $x + 2\geq0$, i.e., $x\geq - 2$. When $x=-2$, $y = 0$.

Step4: Observe the graph

The graph has an $x$-intercept at a positive $x$-value. For $y=\sqrt{x - 2}$, when $x = 2$, $y = 0$. For $y=\sqrt{x+2}$, when $x=-2$, $y = 0$. The graph starts at a positive $x$-value on the $x$-axis, so the function is $y=\sqrt{x - 2}$.

Answer:

$y=\sqrt{x - 2}$