To complete the table for the function \( y = 6^x \), we will calculate the values of \( y \) for the given \( x \) values:
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For \( x = -1 \): \[ y = 6^{-1} = \frac{1}{6} \approx 0.1667 \]
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For \( x = 0 \): \[ y = 6^{0} = 1 \]
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For \( x = 1 \): \[ y = 6^{1} = 6 \]
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For \( x = 2 \): \[ y = 6^{2} = 36 \]
Now the completed table looks like this:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & \frac{1}{6} \approx 0.1667 \ 0 & 1 \ 1 & 6 \ 2 & 36 \ \hline \end{array} \]
Points to Plot
- For \( x = -1, y \approx 0.1667 \) (or \( \frac{1}{6} \))
- For \( x = 0, y = 1 \)
Graphing
To graph the function \( y = 6^x \):
- Point 1: \( (-1, 0.1667) \)
- Point 2: \( (0, 1) \)
As \( x \) increases, \( y \) will grow rapidly due to the exponential nature of the function. You can continue plotting additional points if needed, but these two points are sufficient to begin sketching the graph.
When you sketch the graph, you will notice that as \( x \) goes negative, \( y \) approaches zero, and as \( x \) increases, \( y \) increases steeply. You can also observe that the curve will not touch the x-axis but will get infinitely close.
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