Let's complete the table step by step by evaluating each function at the given values of $x$.

Given functions:

$f(x) = |x - 3| - 4$ $g(x) = 3x - 5$

Step 1: Compute $f(x)$ and $g(x)$ for each $x$.

For $x = 0$: $f(0) = |0 - 3| - 4 = | -3 | - 4 = 3 - 4 = -1$ $g(0) = 3(0) - 5 = 0 - 5 = -5$

For $x = 1$: $f(1) = |1 - 3| - 4 = | -2 | - 4 = 2 - 4 = -2$ $g(1) = 3(1) - 5 = 3 - 5 = -2$

For $x = 2$: $f(2) = |2 - 3| - 4 = | -1 | - 4 = 1 - 4 = -3$ $g(2) = 3(2) - 5 = 6 - 5 = 1$

For $x = 3$: $f(3) = |3 - 3| - 4 = |0| - 4 = 0 - 4 = -4$ $g(3) = 3(3) - 5 = 9 - 5 = 4$

For $x = 4$: $f(4) = |4 - 3| - 4 = |1| - 4 = 1 - 4 = -3$ $g(4) = 3(4) - 5 = 12 - 5 = 7$

Completed Table:

$x$	$f(x)$	$g(x)$
0	-1	-5
1	-2	-2
2	-3	1
3	-4	4
4	-3	7

Step 2: Solve $f(x) = g(x)$

We find that $f(x) = g(x)$ when $x = 1$, since: $f(1) = -2, \quad g(1) = -2$

Thus, the equation $f(x) = g(x)$ has a solution at $x = 1$.

---

Would you like a graphical explanation of this solution? Here are some related questions:

1. How do you determine where two functions are equal algebraically?
2. What is the geometric interpretation of $f(x) = g(x)$?
3. Can we solve $f(x) = g(x)$ without making a table?
4. How does the absolute value function affect the behavior of $f(x)$?
5. What happens if we extend the table to more values of $x$?

Tip: When comparing two functions, their intersection points give the solutions to $f(x) = g(x)$.