Question

Representing Functions Quick Check
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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 inputs \(-4, -2, 0, 2, 4\), we first need to calculate the output for each input using the function.

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 examine the provided options and check if a graph corresponds to these points.

Looking at the outputs calculated:
- The x-values range between \(-4\) and \(4\).
- The y-values range from \(-45\) to \(51\), which is a very wide range, suggesting that the y-axis will need to have significant values for both ranges.

Among the options you provided, the one with the x-axis ranging from \(-4\) to \(4\) and the y-axis from approximately \(-50\) to \(60\) would be a valid candidate to capture all points accurately, especially since most others seem limited.

Unfortunately, since I cannot see the graphs directly, I recommend selecting the graph with the x-axis ranging from \(-4\) to \(4\) and a sufficient y-axis range to include the output values computed above. This is more likely to correctly represent the function \( f(x) = 12x + 3 \) with the specified inputs.