To determine which graph accurately represents the function \( f(x) = 12x + 3 \) using input-output tables, we first need to calculate the output (f(x)) for given inputs of \( -4, -2, 0, 2, \) and \( 4 \).
Let's compute the outputs:
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For \( x = -4 \): \[ f(-4) = 12(-4) + 3 = -48 + 3 = -45 \]
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For \( x = -2 \): \[ f(-2) = 12(-2) + 3 = -24 + 3 = -21 \]
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For \( x = 0 \): \[ f(0) = 12(0) + 3 = 0 + 3 = 3 \]
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For \( x = 2 \): \[ f(2) = 12(2) + 3 = 24 + 3 = 27 \]
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For \( x = 4 \): \[ f(4) = 12(4) + 3 = 48 + 3 = 51 \]
Now, we can compile these results into an input-output table:
| \(x\) | \(f(x)\) | |--------|-----------| | -4 | -45 | | -2 | -21 | | 0 | 3 | | 2 | 27 | | 4 | 51 |
Now, you would compare this table with the graphs available. Look for a graph that has the following points represented:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
The correct graph will plot these points accurately. If you can't see the graphs, identify the one that matches these coordinates.
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