Question
Use input-output tables to determine which graph accurately represents the function f(x)=12x+3
𝑓
(
𝑥
)
=
1
2
𝑥
+
3
with inputs of −4
−
4
, −2
−
2
, 0, 2, and 4.(1 point)
Responses
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.
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.
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.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed pas
𝑓
(
𝑥
)
=
1
2
𝑥
+
3
with inputs of −4
−
4
, −2
−
2
, 0, 2, and 4.(1 point)
Responses
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.
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.
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.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed pas
Answers
Answered by
GPT-4o mini
To determine which graph accurately represents the function \( f(x) = 12x + 3 \), we first need to compute the output values for the given inputs \( -4, -2, 0, 2, \) and \( 4 \).
Let's compute the values:
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 input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Now we can analyze the options provided. Based on the input-output pairs, the graph should show that for negative x-values, f(x) is also negative, with very steep values that increase sharply for positive x.
Looking at the descriptions of the images:
1. If any of the graphs represent values near \( (-4, -45) \) and show a line that dramatically increases past \( (2, 27) \) and includes \( (4, 51) \), that would be the correct choice.
2. The second graph has ranges that might suggest that it does not capture the required range since significant values are beyond the specified y-axis ranges.
Given this analysis, you should look for a graph that captures the range of values derived from the calculations above accurately showing the relationships as described, particularly with steep increases that occur at positive x values.
Please review the graphs and select the one that represents these output values based on prior calculations.
Let's compute the values:
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 input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)
Now we can analyze the options provided. Based on the input-output pairs, the graph should show that for negative x-values, f(x) is also negative, with very steep values that increase sharply for positive x.
Looking at the descriptions of the images:
1. If any of the graphs represent values near \( (-4, -45) \) and show a line that dramatically increases past \( (2, 27) \) and includes \( (4, 51) \), that would be the correct choice.
2. The second graph has ranges that might suggest that it does not capture the required range since significant values are beyond the specified y-axis ranges.
Given this analysis, you should look for a graph that captures the range of values derived from the calculations above accurately showing the relationships as described, particularly with steep increases that occur at positive x values.
Please review the graphs and select the one that represents these output values based on prior calculations.