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.

1 answer

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.