To find the coordinates for the exponential function \( f(x) = (0.4)^x \), we will calculate \( f(x) \) for the specified values of \( x \).
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For \( x = -1 \): \[ f(-1) = (0.4)^{-1} = \frac{1}{(0.4)} = 2.5 \]
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For \( x = 0 \): \[ f(0) = (0.4)^0 = 1 \]
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For \( x = 1 \): \[ f(1) = (0.4)^1 = 0.4 \]
Now, we can summarize the values in a table:
| \( x \) | \( y = f(x) \) | |---------|----------------| | -1 | 2.5 | | 0 | 1 | | 1 | 0.4 |
So, the completed table of coordinates is:
- For \( x = -1 \), \( y = 2.5 \)
- For \( x = 0 \), \( y = 1 \)
- For \( x = 1 \), \( y = 0.4 \)
Sketch of the Graph:
The graph of the function \( f(x) = (0.4)^x \) is a decreasing exponential function. It starts from a high value when \( x \) is negative and approaches zero as \( x \) increases.
- At \( x = -1 \), \( y = 2.5 \)
- At \( x = 0 \), \( y = 1 \)
- At \( x = 1 \), \( y = 0.4 \)
It will pass through these points, decreasing toward the x-axis but never touching it (as \( x \) continues to grow).