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:
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For \( x = -2 \): \[ y = 4 \left( \frac{1}{6} \right)^{-2} = 4 \cdot \left( 6 \right)^2 = 4 \cdot 36 = 144 \]
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For \( x = -1 \): \[ y = 4 \left( \frac{1}{6} \right)^{-1} = 4 \cdot 6 = 24 \]
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For \( x = 0 \): \[ y = 4 \left( \frac{1}{6} \right)^{0} = 4 \cdot 1 = 4 \]
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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 \( x = 1 \):
- \( (-2, 144) \)
- \( (1, \frac{2}{3}) \) 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.