Question

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.

Answer 1

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 output values for each of 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 input-output pairs:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)

Next, we need to check which graph correctly represents these points.

The second and third options both indicate that the x-axis ranges from \(-4\) to \(4\), which is appropriate for our input values. However, we also need to check whether they include the corresponding y-values.

### Analyzing the ranges:
- For \( x = -4 \), \( y = -45 \) (out of range if the y-axis only goes to -10)
- For \( x = -2 \), \( y = -21 \) (also out of range)
- For \( x = 0 \), \( y = 3 \) (within the range of -10 to 10)
- For \( x = 2 \), \( y = 27 \) (out of range)
- For \( x = 4 \), \( y = 51 \) (out of range)

Since the output values exceed the expected y-axis limits in the graphs given, we would need a graph that can display values much lower than -10 and much higher than 10 to include the points computed.

### Conclusion:
None of the provided graphs correctly represents the function \( f(x)=12x+3 \) based on the calculated values. You need to select the graph that covers the range of y-values that include -45, -21, and possibly even up to 51 to depict all the output values correctly. If the y-axis goes no lower than -10 or no higher than 10, then it is impossible to accurately display this linear function properly in any of the graphs described.