To create a table of coordinates for the function \( f(x) = 3^x \), we will calculate the value of the function for each designated \( x \) value. Here's how you can do it for the provided \( x \) values: -2, -1, 0, 1, 2.
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For \( x = -2 \): \[ f(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \]
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For \( x = -1 \): \[ f(-1) = 3^{-1} = \frac{1}{3} \]
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For \( x = 0 \): \[ f(0) = 3^0 = 1 \]
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For \( x = 1 \): \[ f(1) = 3^1 = 3 \]
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For \( x = 2 \): \[ f(2) = 3^2 = 9 \]
Now we can fill out the table:
| \( x \) | \( y = f(x) \) | |:-----------:|:------------------:| | -2 | \( \frac{1}{9} \) | | -1 | \( \frac{1}{3} \) | | 0 | \( 1 \) | | 1 | \( 3 \) | | 2 | \( 9 \) |
Summary of the Coordinates:
- \( (-2, \frac{1}{9}) \)
- \( (-1, \frac{1}{3}) \)
- \( (0, 1) \)
- \( (1, 3) \)
- \( (2, 9) \)
You can now use these calculations to plot the function on a graph!
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