To complete the table for the function \( y = 2^x \), we can substitute the given values of \( x \) into the function.
Let's calculate the values:
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For \( x = -1 \): \[ y = 2^{-1} = \frac{1}{2} = 0.5 \]
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For \( x = 0 \): \[ y = 2^0 = 1 \]
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For \( x = 1 \): \[ y = 2^1 = 2 \]
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For \( x = 2 \): \[ y = 2^2 = 4 \]
Now, we can complete the table:
\[ \begin{array}{|c|c|} \hline x & y \ \hline -1 & 0.5 \ 0 & 1 \ 1 & 2 \ 2 & 4 \ \hline \end{array} \]
Points to Plot
The two points we can plot from our table are:
- \( (-1, 0.5) \)
- \( (2, 4) \)
Graphing the function
To graph the function \( y = 2^x \), we can plot these points on a coordinate system and draw a smooth curve that represents the exponential growth.
- Point (-1, 0.5): This is located to the left of the y-axis just above the x-axis.
- Point (2, 4): This point is located to the right of the y-axis and above the fourth unit on the y-axis.
As the x values increase, \( y = 2^x \) rises rapidly, leading to a steep upward curve. The function approaches but never touches the x-axis as \( x \) decreases (indicating it approaches 0 but is never negative).
Summary of the Graph
The graph of the function starts from just above the x-axis on the left (at \( x = -1, y = 0.5 \)) and rises sharply as \( x \) increases, going through the point \( (2, 4) \).
You can plot these points on graph paper or using graphing software to visualize the exponential growth of the function \( y = 2^x \).