Question

y = √x - 1
y = √x
y = -√x
y = √x + 1
which equation describes the graph?

Explanation:

Step1: Analyze domain of functions

For $y = \sqrt{x}$, domain is $x\geq0$. For $y=\sqrt{x - 1}$, domain is $x\geq1$. For $y=-\sqrt{x}$, domain is $x\geq0$ and it's a reflection of $y = \sqrt{x}$ over $x - axis$. For $y=\sqrt{x + 1}$, domain is $x\geq - 1$.

Step2: Check graph - intercepts

The graph seems to start at the origin $(0,0)$. The function $y=\sqrt{x}$ starts at $(0,0)$ since when $x = 0$, $y=\sqrt{0}=0$.

Step3: Analyze shape of graph

The graph of $y=\sqrt{x}$ has a characteristic shape that increases as $x$ increases. The other functions $y=\sqrt{x - 1}$ is shifted 1 unit to the right, $y =-\sqrt{x}$ is a downward - opening version of $y=\sqrt{x}$, and $y=\sqrt{x + 1}$ is shifted 1 unit to the left. The given graph matches the shape of $y=\sqrt{x}$.

Answer:

$y=\sqrt{x}$