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.(

Answer 1

To determine which graph accurately represents the function \( f(x) = 12x + 3 \) with the specified inputs, we first need to calculate the outputs for each given input using the function.

Let's calculate \( f(x) \) for each of the 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 we can summarize the input-output pairs in a table:

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

Next, we can plot these points and find which graph matches.

**Points:**
- (-4, -45)
- (-2, -21)
- (0, 3)
- (2, 27)
- (4, 51)

Now you would look at the provided graphs and see which one includes all of those points. The correct graph should reflect a steep upward slope due to the coefficient of \( x \) being 12, indicating it is a linear function with a positive slope. The graph should pass through all of the calculated points mentioned above.