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 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.
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Answer 1

To determine which graph accurately represents the function \( f(x) = 12x + 3 \) for the inputs \( -4, -2, 0, 2, \) and \( 4 \), we first need to calculate the corresponding \( f(x) \) values for each input:

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 a set of points:
- \( (-4, -45) \)
- \( (-2, -21) \)
- \( (0, 3) \)
- \( (2, 27) \)
- \( (4, 51) \)

Next, we need to consider the characteristics of the graph based on these points:

- The x-values range from \( -4 \) to \( 4 \).
- The y-values, calculated, are quite high (especially for \( x = 2 \) and \( x = 4 \)), indicating that the graph extends significantly in the positive y-direction.

Given these points, you would look for a graph that includes:
- x-axis ranging at least from \( -4 \) to \( 4 \).
- y-axis capable of showing values down to \(-45\) and up to \(51\).

From the descriptions provided, the first and fourth response both describe graphs with suitable x-axes. However, the key to resolving the suitable graph lies in the y-range. The graph must cover from approximately \( -45 \) to \( 51\).

If all graphs indeed represent a similar interval range but the y-range is not accurately mentioned, you could determine the correctness based purely on their x-axes (since ranges vary).

You will need to double-check which graph's y-axis reaches the necessary points to make a definitive choice. Based on the calculations, the graph must include points through which the calculated output points can also be correctly plotted particularly highlighting the significant y-values.

Please reference these calculated points with the graphical representations to confirm which one meets all criteria.