To complete the table for the function \( y = 9^x \), we will calculate the values of \( y \) for each given value of \( x \):
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For \( x = -1 \): \[ y = 9^{-1} = \frac{1}{9} \approx 0.1111 \]
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For \( x = 0 \): \[ y = 9^0 = 1 \]
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For \( x = 1 \): \[ y = 9^1 = 9 \]
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For \( x = 2 \): \[ y = 9^2 = 81 \]
Now, we can complete the table:
| \( x \) | \( y \) | |---------|------------| | -1 | 0.1111 | | 0 | 1 | | 1 | 9 | | 2 | 81 |
Two Points to Graph the Function
From the table, we can choose the following two points to graph the function:
- \( (0, 1) \)
- \( (1, 9) \)
Graphing the Function
To plot the two points:
- Plot the point \( (0, 1) \) on the coordinate plane.
- Plot the point \( (1, 9) \).
The graph of the function \( y = 9^x \) will show an exponential growth curve, starting from \( (0, 1) \) and rapidly increasing as \( x \) increases.
If you were to graph a larger portion of this function, you would see that it approaches \( 0 \) as \( x \) goes to \( -\infty \) and rises steeply for positive values of \( x \).
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