To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the specified inputs, we first need to calculate the outputs for each given input using the function.
Let's calculate \( f(x) \) for each of the inputs:
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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 summarize the input-output pairs in a table:
| \( x \) | \( f(x) \) | |---------|------------| | -4 | -45 | | -2 | -21 | | 0 | 3 | | 2 | 27 | | 4 | 51 |
Next, we can plot these points and find which graph matches.
Points:
- (-4, -45)
- (-2, -21)
- (0, 3)
- (2, 27)
- (4, 51)
Now you would look at the provided graphs and see which one includes all of those points. The correct graph should reflect a steep upward slope due to the coefficient of \( x \) being 12, indicating it is a linear function with a positive slope. The graph should pass through all of the calculated points mentioned above.