To complete the table for the function \( y = \left(\frac{1}{3}\right)^x \), we will calculate the value of \( y \) for each given value of \( x \).
Table
| \( x \) | \( y = \left(\frac{1}{3}\right)^x \) | |---------|-------------------------------------| | -2 | \( \left(\frac{1}{3}\right)^{-2} = 3^2 = 9 \) | | -1 | \( \left(\frac{1}{3}\right)^{-1} = 3^1 = 3 \) | | 0 | \( \left(\frac{1}{3}\right)^{0} = 1 \) | | 1 | \( \left(\frac{1}{3}\right)^{1} = \frac{1}{3} \) |
Completed Table
| \( x \) | \( y \) | |---------|---------| | -2 | 9 | | -1 | 3 | | 0 | 1 | | 1 | \(\frac{1}{3} \approx 0.33\) |
Points to Graph
Now, we can plot two points to graph the function:
- For \( x = -2 \): \( ( -2, 9) \)
- For \( x = -1 \): \( ( -1, 3) \)
Graphing the Function
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Plot the points:
- Point 1: \( (-2, 9) \)
- Point 2: \( (-1, 3) \)
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Draw the curve:
- Using these points, you can now sketch or use graphing software to draw the curve for the function \( y = \left(\frac{1}{3}\right)^x \), which will show a decreasing exponential function starting from a high value as \( x \) approaches negative infinity and converging towards 0 as \( x \) increases.
Note
Since I can't directly draw the graph here, you can use graphing tools like Desmos or graphing calculators to visualize it properly along with the plotted points.