Question

Complete the table for the function y = 4(1/6)^x
x
-2

-1

0

1
Now, graph the function.
Plot two points to graph the function.

Answer 1

To complete the table for the function \( y = 4 \left( \frac{1}{6} \right)^x \), we will evaluate the function for each given \( x \) value. Let's calculate:

1. For \( x = -2 \):
\[
y = 4 \left( \frac{1}{6} \right)^{-2} = 4 \cdot \left( 6 \right)^2 = 4 \cdot 36 = 144
\]

2. For \( x = -1 \):
\[
y = 4 \left( \frac{1}{6} \right)^{-1} = 4 \cdot 6 = 24
\]

3. For \( x = 0 \):
\[
y = 4 \left( \frac{1}{6} \right)^{0} = 4 \cdot 1 = 4
\]

4. For \( x = 1 \):
\[
y = 4 \left( \frac{1}{6} \right)^{1} = 4 \cdot \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \approx 0.67
\]

Now we can summarize the completed table:

| \( x \) | \( y = 4 \left( \frac{1}{6} \right)^x \) |
|---------|-------------------------------------------|
| -2 | 144 |
| -1 | 24 |
| 0 | 4 |
| 1 | \( \frac{2}{3} \) or approximately 0.67 |

### Plotting Points

Using the calculated points, we can pick two points to graph the function. Let's plot the points for \( x = -2 \) and \( x = 1 \):

1. \( (-2, 144) \)
2. \( (1, \frac{2}{3}) \) or \( (1, 0.67) \)

### Graphing

Unfortunately, I cannot physically draw a graph here, but you can visualize or graph on graph paper or using graphing software by:

- Marking point \( (-2, 144) \)
- Marking point \( (1, 0.67) \)
- Drawing the curve that represents the function \( y = 4 \left( \frac{1}{6} \right)^x \), which will show an exponential decay as \( x \) increases. The curve will approach the x-axis but never quite touch it.