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 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.
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.
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 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.
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.
Answers
GPT-4o mini
To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the given inputs (-4, -2, 0, 2, and 4), we need to calculate the output values (y-values) for each input value (x-value) using the equation of the function.
Let's calculate each output:
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 can summarize the input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Based on the output values, we see that the function produces very large y-values for both positive and negative x-values, particularly with y-values reaching -45 and 51.
Among the graph options provided, the one that accurately matches our calculated points must have an x-axis range encompassing at least from -4 to 4, and the y-values must adequately display the corresponding outputs we calculated, which can go as low as -45 and as high as 51.
Therefore, the correct response would be the one that has the x-axis ranging from -4 to 4 and the y-axis ranging from at least -45 to a value greater than or equal to 51.
Since none of the options provided mention the y-axis cap, we assume the appropriate graph to select is one that captures the general signaling of a line through all specified x-values and has a broad enough range to encompass all derived results. Thus identifying which graph it is among the visual options would depend on those visibility features based on the given descriptions.
However, do note if the y-values don’t go high enough based on the ranges that were mentioned in your inputs, it suggests that the answer doesn't perfectly match — you likely should choose one of the graphs that has its x-axis configured similarly to your inputs and has an appropriate vertical y-range.
Let's calculate each output:
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 can summarize the input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Based on the output values, we see that the function produces very large y-values for both positive and negative x-values, particularly with y-values reaching -45 and 51.
Among the graph options provided, the one that accurately matches our calculated points must have an x-axis range encompassing at least from -4 to 4, and the y-values must adequately display the corresponding outputs we calculated, which can go as low as -45 and as high as 51.
Therefore, the correct response would be the one that has the x-axis ranging from -4 to 4 and the y-axis ranging from at least -45 to a value greater than or equal to 51.
Since none of the options provided mention the y-axis cap, we assume the appropriate graph to select is one that captures the general signaling of a line through all specified x-values and has a broad enough range to encompass all derived results. Thus identifying which graph it is among the visual options would depend on those visibility features based on the given descriptions.
However, do note if the y-values don’t go high enough based on the ranges that were mentioned in your inputs, it suggests that the answer doesn't perfectly match — you likely should choose one of the graphs that has its x-axis configured similarly to your inputs and has an appropriate vertical y-range.