To complete the table for the function \( y = 4(0.5)^x \), we can substitute the given \( x \) values into the equation to find the corresponding \( y \) values.
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For \( x = -2 \): \[ y = 4(0.5)^{-2} = 4 \cdot 2^2 = 4 \cdot 4 = 16 \]
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For \( x = -1 \): \[ y = 4(0.5)^{-1} = 4 \cdot 2^1 = 4 \cdot 2 = 8 \]
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For \( x = 0 \): \[ y = 4(0.5)^{0} = 4 \cdot 1 = 4 \]
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For \( x = 1 \): \[ y = 4(0.5)^{1} = 4 \cdot 0.5 = 2 \]
Now we can complete the table:
| x | y | |-----|-----| | -2 | 16 | | -1 | 8 | | 0 | 4 | | 1 | 2 |
Plotting Two Points
Now we can graph the function by plotting two of the calculated points. Let's choose the points \( (-2, 16) \) and \( (1, 2) \):
- Point (-2, 16): This point is located at \( x = -2 \), \( y = 16 \).
- Point (1, 2): This point is located at \( x = 1 \), \( y = 2 \).
When graphing the function on a Cartesian plane, the general shape will be a decreasing exponential curve since the base is less than 1. The graph will show that as \( x \) increases, \( y \) decreases.
These two points can be quite far apart due to the nature of the exponential decay, so you may want to scale your graph accordingly.