The image you uploaded shows a problem related to graphing a function using translations. Specifically, the function is:

$g(x) = \sqrt{x + 1} - 3$

The question asks you to identify the parent function for $g(x)$. The parent function is the most basic form of the given function before any transformations (shifts, reflections, stretches, etc.).

For this problem, the parent function is the square root function $\sqrt{x}$, because the expression inside the square root is $x + 1$, and the "-3" outside the square root represents a vertical translation.

So, the parent function for $g(x) = \sqrt{x + 1} - 3$ is:

$\sqrt{x}$

Would you like to proceed with further parts of the problem or explore more details? Let me know if you have any questions! Here are some related questions:

1. What does the transformation $\sqrt{x + 1}$ represent?
2. How does the transformation $-3$ affect the graph of the square root function?
3. What is the impact of horizontal shifts on the graph of square root functions?
4. How can you graph $g(x) = \sqrt{x + 1} - 3$ step by step?
5. What are some properties of the square root function, like domain and range?

Tip: When identifying transformations, always look at the inside of the function for horizontal shifts and the outside for vertical shifts.