Question

which equation describes the graph? y = √x y = 1/4√x y = -1/4√x y = 4√x

Explanation:

Step1: Analyze square - root function shape

The general form of a square - root function is $y = a\sqrt{x}$, where $a$ determines the vertical stretch or compression and reflection. The graph of $y=\sqrt{x}$ starts at the origin $(0,0)$ and increases.

Step2: Check for vertical stretch/compression

If $|a|> 1$, the graph is vertically stretched. If $0 < |a|<1$, the graph is vertically compressed. If $a<0$, the graph is reflected over the $x$ - axis. The given graph starts at the origin and increases, so $a>0$. Also, it appears to be vertically compressed compared to $y = \sqrt{x}$.

Step3: Evaluate options

For $y=\sqrt{x}$, it is the basic square - root function without compression. For $y = 4\sqrt{x}$, it is vertically stretched. For $y=-\frac{1}{4}\sqrt{x}$, it is reflected over the $x$ - axis. For $y=\frac{1}{4}\sqrt{x}$, it is vertically compressed with $a=\frac{1}{4}>0$.

Answer:

$y=\frac{1}{4}\sqrt{x}$