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.
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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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 outputs for 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 that we have calculated the outputs, we have the following points:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)

Next, we need to check the y values of these outputs against the ranges of the graphs provided in the responses.

From the calculations:
- The y-values of the outputs range from \( -45 \) (for \( x = -4 \)) to \( 51 \) (for \( x = 4 \)).
- Therefore, the graph needs to accommodate y-coordinates ranging from at least \( -45 \) to \( 51 \).

From the response options, we can see that the second graph (with x values from -4 to 4 and y values from -10 to 10) would not be suitable since it does not capture the range needed.

Since all the other options seem similar with the same axes range, none of the provided graphs captures the necessary vertical range. Therefore, you can discard them all because none reflect the correct outputs derived from the function \( f(x) = 12x + 3 \) with the given inputs.

In conclusion, based on the output values and their range, none of the provided graphs accurately represents the function \( f(x) = 12x + 3 \).