Bot GPT 4-o mini To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the given inputs of \( -4, -2, 0, 2, \) and \( 4 \), we first need to calculate the corresponding output values for each of these inputs:
-
For \( x = -4 \): \[ f(-4) = 12(-4) + 3 = -48 + 3 = -45 \]
-
For \( x = -2 \): \[ f(-2) = 12(-2) + 3 = -24 + 3 = -21 \]
-
For \( x = 0 \): \[ f(0) = 12(0) + 3 = 0 + 3 = 3 \]
-
For \( x = 2 \): \[ f(2) = 12(2) + 3 = 24 + 3 = 27 \]
-
For \( x = 4 \): \[ f(4) = 12(4) + 3 = 48 + 3 = 51 \]
Now we have the following input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Next, we need to check which graph correctly represents these points.
The second and third options both indicate that the x-axis ranges from \(-4\) to \(4\), which is appropriate for our input values. However, we also need to check whether they include the corresponding y-values.
Analyzing the ranges:
- For \( x = -4 \), \( y = -45 \) (out of range if the y-axis only goes to -10)
- For \( x = -2 \), \( y = -21 \) (also out of range)
- For \( x = 0 \), \( y = 3 \) (within the range of -10 to 10)
- For \( x = 2 \), \( y = 27 \) (out of range)
- For \( x = 4 \), \( y = 51 \) (out of range)
Since the output values exceed the expected y-axis limits in the graphs given, we would need a graph that can display values much lower than -10 and much higher than 10 to include the points computed.
Conclusion:
None of the provided graphs correctly represents the function \( f(x)=12x+3 \) based on the calculated values. You need to select the graph that covers the range of y-values that include -45, -21, and possibly even up to 51 to depict all the output values correctly. If the y-axis goes no lower than -10 or no higher than 10, then it is impossible to accurately display this linear function properly in any of the graphs described.
1 answer