Question

write the function shown in the graph to the right.
write the function that describes the graph above.
$y = \square$(simplify your answer.)

Explanation:

Step1: Identify function type

The graph is a horizontal shift of a square root function, which has the form $y=\sqrt{x-h}+k$, where $(h,k)$ is the starting point of the curve.

Step2: Locate the starting point

The curve starts at $(-4, 0)$, so $h=-4$, $k=0$.

Step3: Substitute values into formula

Substitute $h=-4$ and $k=0$ into the function:
$y=\sqrt{x-(-4)}+0 = \sqrt{x+4}$

Step4: Verify with a point

Check the point $(0,2)$: $\sqrt{0+4}=\sqrt{4}=2$, which matches the graph.

Answer:

$\boldsymbol{y=\sqrt{x+4}}$