Question
Use input-output tables to determine which graph accurately represents the function f(x)=12x+3 with inputs of −4 , −2 , 0, 2, and 4.(1 point)
Responses
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
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Responses
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
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Answers
GPT-4o 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 outputs for these inputs.
1. For \( x = -4 \):
\[
f(-4) = 12(-4) + 3 = -48 + 3 = -45
\]
2. For \( x = -2 \):
\[
f(-2) = 12(-2) + 3 = -24 + 3 = -21
\]
3. For \( x = 0 \):
\[
f(0) = 12(0) + 3 = 0 + 3 = 3
\]
4. For \( x = 2 \):
\[
f(2) = 12(2) + 3 = 24 + 3 = 27
\]
5. For \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
Now we have the following points based on the inputs and their corresponding outputs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Next, we need to check which of the provided graphs represents these points:
- The first three graphs span the range of x from \(-4\) to \(4\) and y from approximately \(-10\) to \(10\), which would not capture the outputs we found (such as \( -45 \) and \( 51 \)).
- The fourth graph spans from \(0\) to \(7\) on the x-axis and from \(-5\) to \(5\) on the y-axis, which also wouldn’t capture our output values as they are well outside this range.
Given this analysis, none of the graphs provided would accurately represent the function \( f(x) = 12x + 3 \) for the given inputs, since all output values we computed (such as \(-45\) and \(51\)) fall outside the y-axis ranges indicated in the graphs.
More conveniently, it seems that all options listed do not reveal a correct graph for the computed function outputs under the specified inputs.
1. For \( x = -4 \):
\[
f(-4) = 12(-4) + 3 = -48 + 3 = -45
\]
2. For \( x = -2 \):
\[
f(-2) = 12(-2) + 3 = -24 + 3 = -21
\]
3. For \( x = 0 \):
\[
f(0) = 12(0) + 3 = 0 + 3 = 3
\]
4. For \( x = 2 \):
\[
f(2) = 12(2) + 3 = 24 + 3 = 27
\]
5. For \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
Now we have the following points based on the inputs and their corresponding outputs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Next, we need to check which of the provided graphs represents these points:
- The first three graphs span the range of x from \(-4\) to \(4\) and y from approximately \(-10\) to \(10\), which would not capture the outputs we found (such as \( -45 \) and \( 51 \)).
- The fourth graph spans from \(0\) to \(7\) on the x-axis and from \(-5\) to \(5\) on the y-axis, which also wouldn’t capture our output values as they are well outside this range.
Given this analysis, none of the graphs provided would accurately represent the function \( f(x) = 12x + 3 \) for the given inputs, since all output values we computed (such as \(-45\) and \(51\)) fall outside the y-axis ranges indicated in the graphs.
More conveniently, it seems that all options listed do not reveal a correct graph for the computed function outputs under the specified inputs.