Question

Complete the table for the function y= (1/6)^x.
x y
–2
–1
0
1
Now, graph the function.
Plot two points to graph the function.

Answer 1

Let's start by completing the table for the function \( y = \left(\frac{1}{6}\right)^x \) using the given \( x \) values.

### Completing the Table

1. For \( x = -2 \):
\[
y = \left(\frac{1}{6}\right)^{-2} = 6^2 = 36
\]

2. For \( x = -1 \):
\[
y = \left(\frac{1}{6}\right)^{-1} = 6^1 = 6
\]

3. For \( x = 0 \):
\[
y = \left(\frac{1}{6}\right)^0 = 1
\]

4. For \( x = 1 \):
\[
y = \left(\frac{1}{6}\right)^1 = \frac{1}{6} \approx 0.1667
\]

### Completed Table

| \( x \) | \( y \) |
|----------|----------|
| -2 | 36 |
| -1 | 6 |
| 0 | 1 |
| 1 | 0.1667 |

### Graphing the Function

To graph the function, plot the points from the completed table. You can plot the following points on a coordinate grid:

1. Point for \( (-2, 36) \)
2. Point for \( (-1, 6) \)
3. Point for \( (0, 1) \)
4. Point for \( (1, 0.1667) \)

**Note:** Since I cannot graph directly here, I will describe how you can graph them:

- For each pair \( (x, y) \), place a dot at that coordinate on the Cartesian plane.
- Connect the points with a smooth curve, keeping in mind that the function \( y = \left(\frac{1}{6}\right)^x \) will asymptotically approach the x-axis for large \( x \) but never actually touches it (as it approaches zero).

This function will show an exponential decay as \( x \) increases, starting from a high value when \( x \) is negative, and decreasing towards zero as \( x \) becomes positive.