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.
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.
Answers
GPT-4o mini
To determine which graph accurately represents the function \( f(x) = 12x + 3 \) for the given inputs \(-4, -2, 0, 2, \) and \( 4\), we first need to calculate the corresponding output values of the function for each of these inputs.
### Calculate Outputs
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 \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
### Summary of Points
The points we have calculated are:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
### Evaluating the Graphs
Now we need to find a graph that contains these points. The outputs indicate that the y-values become significantly large and negative for the negative x-values, and they rise steeply as \( x \) increases.
Based on the information provided about the axes:
- The first three graphs mention an x-axis ranging from -4 to 4, suggesting they might represent our function as we are evaluating those inputs.
- The last graph lists an x-axis that ranges from 0 to 7, which will not capture the full range of our calculated points.
Given the steepness of the function due to the coefficient of \( x \) being 12, we should look for a graph that captures high y-values as well as low negative ones.
### Conclusion
Based on the values calculated and the characteristics needed in the graph, choose the option that presents the correct range for both axes including x-values from -4 to 4 and y-values sufficiently below -45 and over 51, If you're unsure about the specific look of the graphs described but see one with this range, that’s the one that represents the function accurately.
### Calculate Outputs
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 \( x = 4 \):
\[
f(4) = 12(4) + 3 = 48 + 3 = 51
\]
### Summary of Points
The points we have calculated are:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
### Evaluating the Graphs
Now we need to find a graph that contains these points. The outputs indicate that the y-values become significantly large and negative for the negative x-values, and they rise steeply as \( x \) increases.
Based on the information provided about the axes:
- The first three graphs mention an x-axis ranging from -4 to 4, suggesting they might represent our function as we are evaluating those inputs.
- The last graph lists an x-axis that ranges from 0 to 7, which will not capture the full range of our calculated points.
Given the steepness of the function due to the coefficient of \( x \) being 12, we should look for a graph that captures high y-values as well as low negative ones.
### Conclusion
Based on the values calculated and the characteristics needed in the graph, choose the option that presents the correct range for both axes including x-values from -4 to 4 and y-values sufficiently below -45 and over 51, If you're unsure about the specific look of the graphs described but see one with this range, that’s the one that represents the function accurately.