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

Answer 1

To determine which graph represents the function \( f(x) = 12x + 3 \) for the specified inputs, we need to compute the output values for each given input.

Let's calculate \( f(x) \) for the inputs \( -4, -2, 0, 2, \) and \( 4 \).

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 create the input-output table:

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

Now that we have the output values, you can compare these values with the graphs available to determine which graph accurately represents the function \( f(x) = 12x + 3 \).

Looking for the points:
- (-4, -45)
- (-2, -21)
- (0, 3)
- (2, 27)
- (4, 51)

Select the graph that passes through these points to confirm if it matches the function representation.