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)

Answer 1

To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the given inputs, we can create an input-output table by calculating the output for each input value.

Here are the calculations 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 can summarize these input-output pairs in a table:

| \( x \) | \( f(x) \) |
|---------|------------|
| -4 | -45 |
| -2 | -21 |
| 0 | 3 |
| 2 | 27 |
| 4 | 51 |

Now, we have the following coordinates based on the calculations:
- (-4, -45)
- (-2, -21)
- (0, 3)
- (2, 27)
- (4, 51)

To find the correct graph, look for a graph that contains all these points. The output values increase very steeply because of the slope of 12 in the function.

Please check the graphs provided to see which one accurately plots these points.