We are given a linear function $g(x) = \frac{7}{2}x$ and a table. We need to complete the table with the corresponding values of $g(x)$ for given values of $x$ and vice-versa.

1. Problem Description

We are given a linear function $g(x) = \frac{7}{2}x$ and a table. We need to complete the table with the corresponding values of $g(x)$ for given values of $x$ and vice-versa.

2. Solution Steps

First, let's find $g(0)$.

$g(0) = \frac{7}{2}(0) = 0$

Next, let's find $g(-2)$.

$g(-2) = \frac{7}{2}(-2) = -7$

Now, we need to find the $x$ value for which $g(x) = 21$.

We have $\frac{7}{2}x = 21$.

Multiplying both sides by $\frac{2}{7}$, we get $x = 21 \times \frac{2}{7} = 3 \times 2 = 6$.

Finally, we need to find the $x$ value for which $g(x) = -31.5$.

We have $\frac{7}{2}x = -31.5$.

Multiplying both sides by $\frac{2}{7}$, we get $x = -31.5 \times \frac{2}{7} = -63/10 \times 2/7 = -9/5 \times 2 = -9$.

So, $x = -9$.

3. Final Answer

The completed table is:

x | 0 | -2 | 6 | -9

---|---|---|---|---

g(x) | 0 | -7 | 21 | -31.5