The function given in the image is:

$f(x) = \sqrt{x + 9}$

To fill in the table, we will substitute each $x$ value from the table into this function. If $x + 9$ is negative, then $f(x)$ will not be a real number (since we cannot take the square root of a negative number in the set of real numbers).

Let’s go through each value of $x$ in the table:

1. For $x = -14$: $f(-14) = \sqrt{-14 + 9} = \sqrt{-5}$ Since $-5$ is negative, $f(-14)$ is not a real number.

2. For $x = -9$: $f(-9) = \sqrt{-9 + 9} = \sqrt{0} = 0$

3. For $x = -5$: $f(-5) = \sqrt{-5 + 9} = \sqrt{4} = 2$

So, the table should be filled in as follows:

Would you like further details on these calculations or have any questions?

Related Questions:

1. What would the function output for values of $x$ greater than 0?
2. How would you graph this square root function?
3. What is the domain of $f(x) = \sqrt{x + 9}$?
4. How can you determine whether other functions have non-real values?
5. What transformations are applied to the basic square root function to get $f(x) = \sqrt{x + 9}$?

Tip:

To find the domain of any square root function, ensure the expression inside the square root is non-negative.