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 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.
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.
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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 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.
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.
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Answers
GPT-4o mini
To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the specified inputs of \( -4 \), \( -2 \), \( 0 \), \( 2 \), and \( 4 \), we first need to calculate the output values for each input using the function.
1. **Calculate the output values:**
- 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 \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
2. **List the input-output pairs:**
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
3. **Assessing the outputs:**
We observe that for these inputs, the outputs are quite large negative numbers for the negative inputs and large positive numbers for the positive inputs.
4. **Look at the graphs:**
Since we can't physically see the graphs, we can infer that:
- The graph must reflect large negative values (around -45) for \( x = -4 \) and smaller negative values for \( x = -2 \).
- There will be a positive output (3) for \( x = 0 \), and large positive values for \( x = 2 \) (27) and \( x = 4 \) (51).
5. **Determine which graph fits these points:**
You'll need to confirm which listed graph passes through the points you calculated and matches this behavior on the coordinate plane. Look for a graph that shows:
- A steep upward trend (consistent with the large slope of 12),
- The specific points where:
- \( x = -4 \) corresponds to \( y = -45 \),
- \( x = -2 \) corresponds to \( y = -21 \),
- \( x = 0 \) corresponds to \( y = 3 \),
- \( x = 2 \) corresponds to \( y = 27 \),
- \( x = 4 \) corresponds to \( y = 51 \).
Based on this analysis, select the graph that meets these criteria.
1. **Calculate the output values:**
- 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 \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
2. **List the input-output pairs:**
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
3. **Assessing the outputs:**
We observe that for these inputs, the outputs are quite large negative numbers for the negative inputs and large positive numbers for the positive inputs.
4. **Look at the graphs:**
Since we can't physically see the graphs, we can infer that:
- The graph must reflect large negative values (around -45) for \( x = -4 \) and smaller negative values for \( x = -2 \).
- There will be a positive output (3) for \( x = 0 \), and large positive values for \( x = 2 \) (27) and \( x = 4 \) (51).
5. **Determine which graph fits these points:**
You'll need to confirm which listed graph passes through the points you calculated and matches this behavior on the coordinate plane. Look for a graph that shows:
- A steep upward trend (consistent with the large slope of 12),
- The specific points where:
- \( x = -4 \) corresponds to \( y = -45 \),
- \( x = -2 \) corresponds to \( y = -21 \),
- \( x = 0 \) corresponds to \( y = 3 \),
- \( x = 2 \) corresponds to \( y = 27 \),
- \( x = 4 \) corresponds to \( y = 51 \).
Based on this analysis, select the graph that meets these criteria.