Bot GPT 4-o mini To determine which graph represents the function \( f(x) = 12x + 3 \) for the specified inputs, we need to compute the output values for each given input.
Let's calculate \( f(x) \) for the inputs \( -4, -2, 0, 2, \) and \( 4 \).
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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 create the input-output table:
| \( x \) | \( f(x) \) | |:---------:|:-----------:| | -4 | -45 | | -2 | -21 | | 0 | 3 | | 2 | 27 | | 4 | 51 |
Now that we have the output values, you can compare these values with the graphs available to determine which graph accurately represents the function \( f(x) = 12x + 3 \).
Looking for the points:
- (-4, -45)
- (-2, -21)
- (0, 3)
- (2, 27)
- (4, 51)
Select the graph that passes through these points to confirm if it matches the function representation.
1 answer