write the function shown in the graph to the right.\n\nwrite the function that describes the graph above.\ny…

Explanation:

Step1: Identify function type

The graph is a square root curve, shifted horizontally. The parent function is $y=\sqrt{x}$.

Step2: Find horizontal shift

The vertex of the parent $y=\sqrt{x}$ is at $(0,0)$. This graph's vertex is at $(-4, 0)$, so it is shifted left 4 units. For a left shift of $h$ units, the form is $y=\sqrt{x+h}$. Here $h=4$, so the function is $y=\sqrt{x+4}$.

Step3: Verify with a point

Take $x=0$: $y=\sqrt{0+4}=2$. The graph passes through $(0,2)$, which matches. Take $x=5$: $y=\sqrt{5+4}=3$, which also aligns with the curve's trend.

Answer:

$\sqrt{x+4}$