To solve the function $f(x) = \sqrt{x + 3} + 4$ and complete the table, we will evaluate $f(x)$ for each value of $x$ provided in the table.

Step-by-Step Calculations:

1. For $x = -3$: $f(-3) = \sqrt{-3 + 3} + 4 = \sqrt{0} + 4 = 0 + 4 = 4$ So, $y = 4$ when $x = -3$.

2. For $x = -2$: $f(-2) = \sqrt{-2 + 3} + 4 = \sqrt{1} + 4 = 1 + 4 = 5$ So, $y = 5$ when $x = -2$.

3. For $x = 1$: $f(1) = \sqrt{1 + 3} + 4 = \sqrt{4} + 4 = 2 + 4 = 6$ So, $y = 6$ when $x = 1$.

4. For $x = 6$: $f(6) = \sqrt{6 + 3} + 4 = \sqrt{9} + 4 = 3 + 4 = 7$ So, $y = 7$ when $x = 6$.

Completed Table:

Would you like more details or have any questions?

Here are some related questions:

1. What happens to $f(x)$ as $x$ increases further?
2. How does the function $f(x) = \sqrt{x + 3} + 4$ behave for negative values of $x$?
3. What is the domain of the function $f(x) = \sqrt{x + 3} + 4$?
4. How would the function change if the constant added outside the square root was different?
5. What is the range of $f(x) = \sqrt{x + 3} + 4$?

Tip: When dealing with square root functions, always check that the expression under the square root is non-negative to ensure the function is defined.