To find the horizontal reflection of the function \( f(x) = x^3 \), we need to replace \( x \) with \( -x \).
Part A:
The new function after the horizontal reflection is: \[ f(x) = (-x)^3 = -x^3 \]
Part B:
We need to complete the table for the function \( -f(x) = -x^3 \). First, let's calculate \( -f(x) \) for the given values of \( x \):
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For \( x = -3 \): \[ -f(-3) = -(-3)^3 = -(-27) = 27 \]
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For \( x = -2 \): \[ -f(-2) = -(-2)^3 = -(-8) = 8 \]
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For \( x = -1 \): \[ -f(-1) = -(-1)^3 = -(-1) = 1 \]
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For \( x = 0 \): \[ -f(0) = -(0)^3 = 0 \]
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For \( x = 1 \): \[ -f(1) = -(1)^3 = -1 \]
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For \( x = 2 \): \[ -f(2) = -(2)^3 = -8 \]
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For \( x = 3 \): \[ -f(3) = -(3)^3 = -27 \]
Now let's complete the table.
| x | -f(x) | |------|-------| | -3 | 27 | | -2 | 8 | | -1 | 1 | | 0 | 0 | | 1 | -1 | | 2 | -8 | | 3 | -27 |
So the completed table for \( -f(x) \) is:
| x | -f(x) | |------|-------| | -3 | 27 | | -2 | 8 | | -1 | 1 | | 0 | 0 | | 1 | -1 | | 2 | -8 | | 3 | -27 |
2 answers