Question

which equation describes the graph? y = √x + 4 y = √x - 4 y = √x - 4 y = √x + 4

Explanation:

Step1: Analyze domain of square - root functions

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

Step2: Check the domain of $y=\sqrt{x + 4}$

Set $x+4\geq0$, then $x\geq - 4$. The graph of $y = \sqrt{x + 4}$ starts at $x=-4$.

Step3: Check the domain of $y=\sqrt{x - 4}$

Set $x - 4\geq0$, then $x\geq4$. The graph of $y=\sqrt{x - 4}$ starts at $x = 4$.

Step4: Analyze the given graph

The graph starts at $x = 4$. So the function is $y=\sqrt{x - 4}$.

Answer:

$y=\sqrt{x - 4}$