Question

the graph of $y = \sqrt{x}$ is the solid black graph below. which function represents the dotted graph?\
graph\
answer\
$\circ$ $y = \sqrt{x - 4} + 4$ $\circ$ $y = \sqrt{x - 4} - 4$\
$\circ$ $y = \sqrt{x + 4} + 4$ $\circ$ $y = \sqrt{x + 4} - 4$\
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Explanation:

Step1: Identify parent function vertex

The parent function $y=\sqrt{x}$ has a vertex at $(0,0)$.

Step2: Locate dotted graph vertex

The dotted graph's vertex is at $(4,-4)$.

Step3: Apply horizontal/vertical shifts

For a right shift by $h$ and down shift by $k$, the transformed function is $y=\sqrt{x-h}-k$. Here $h=4$, $k=4$, so $y=\sqrt{x-4}-4$.

Step4: Verify with a point

Test $x=8$: parent gives $y=2$, dotted gives $y=-2$. Substitute $x=8$ into $y=\sqrt{x-4}-4$: $\sqrt{8-4}-4=2-4=-2$, which matches.

Answer:

$y = \sqrt{x - 4} - 4$