To complete the table for the translated function \( y = f(x + 5) \), we need to find the corresponding \( y \) values for each of the translated \( x \) values in the original function.
The translation \( x + 5 \) means we take each \( x \) value in the original function and subtract 5 to get the corresponding original \( x \) value needed to find \( y \):
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For \( x = -2 \): \[ y = f(-2 + 5) = f(3) \rightarrow \text{(not given, so we can't compute the value)} \]
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For \( x = -1 \): \[ y = f(-1 + 5) = f(4) \rightarrow \text{(not given, so we can't compute the value)} \]
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For \( x = 0 \): \[ y = f(0 + 5) = f(5) \rightarrow 5 \]
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For \( x = 1 \): \[ y = f(1 + 5) = f(6) \rightarrow \text{(not given, so we can't compute the value)} \]
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For \( x = 2 \): \[ y = f(2 + 5) = f(7) \rightarrow \text{(not given, so we can't compute the value)} \]
Since we don't have values for \( f(3) \), \( f(4) \), \( f(6) \), or \( f(7) \), we can only fill in the known value for \( x = 5 \):
For \( x = 5 \): \[ y = f(5 + 5) = f(10) \rightarrow \text{(not given, so we can't compute the value)} \]
Given what we have, let's summarize the tables:
Original Function
| x | y = f(x) | |----|----------| | -2 | 5 | | -1 | 2 | | 0 | 1 | | 1 | 2 | | 2 | 5 |
Translated Function
| x | y = f(x + 5) | |----|------------| | -2 | (not given) | | -1 | (not given) | | 0 | 5 | | 1 | (not given) | | 2 | (not given) | | 5 | (not given) |
Please provide the corresponding values for the function at \( f(3) \), \( f(4) \), \( f(6) \), and \( f(7) \) if available, so the table can be completed.
1 answer