The function given is $f(x) = \sqrt{x - 8}$. Let's compute $f(x)$ for each $x$-value in the table:

1. For $x = 8$: $f(8) = \sqrt{8 - 8} = \sqrt{0} = 0$

2. For $x = 44$: $f(44) = \sqrt{44 - 8} = \sqrt{36} = 6$

3. For $x = 57$: $f(57) = \sqrt{57 - 8} = \sqrt{49} = 7$

4. For $x = 72$: $f(72) = \sqrt{72 - 8} = \sqrt{64} = 8$

Results to fill in the table:

• When $x = 8$, $f(x) = 0$.
• When $x = 44$, $f(x) = 6$.
• When $x = 57$, $f(x) = 7$.
• When $x = 72$, $f(x) = 8$.

Let me know if you want more details or have any questions!

Related Questions:

1. How is the domain of $f(x) = \sqrt{x - 8}$ determined?
2. What would $f(x)$ equal if $x = 7$?
3. How does the graph of $f(x) = \sqrt{x - 8}$ compare to $f(x) = \sqrt{x}$?
4. What is the range of $f(x)$ for the given $x$-values?
5. How do you simplify square roots of non-perfect squares, if $x$ had values like $10$ or $20$?

Tip:

For square root functions, ensure the expression inside the square root ($x - 8$) is non-negative to find valid $x$-values.