We are asked to complete the table for the function $y = \frac{1}{2}(7)^x$ for the given values of $x$: $-1$, $0$, $1$, and $2$.

1. Problem Description

We are asked to complete the table for the function $y = \frac{1}{2}(7)^x$ for the given values of $x$: $-1$, $0$, $1$, and $2$.

2. Solution Steps

We will substitute each value of $x$ into the equation $y = \frac{1}{2}(7)^x$ and calculate the corresponding value of $y$.

Case $x = -1$:

$y = \frac{1}{2}(7)^{-1} = \frac{1}{2} \cdot \frac{1}{7} = \frac{1}{14}$

Case $x = 0$:

$y = \frac{1}{2}(7)^{0} = \frac{1}{2} \cdot 1 = \frac{1}{2}$

Case $x = 1$:

$y = \frac{1}{2}(7)^{1} = \frac{1}{2} \cdot 7 = \frac{7}{2}$

Case $x = 2$:

$y = \frac{1}{2}(7)^{2} = \frac{1}{2} \cdot 49 = \frac{49}{2}$

3. Final Answer

The completed table is:

$x = -1, y = \frac{1}{14}$

$x = 0, y = \frac{1}{2}$

$x = 1, y = \frac{7}{2}$

$x = 2, y = \frac{49}{2}$