Question

Use input out put tables to determine which graph accurately represents the function f (x) = 1/2x + 3 with inputs of -4, -3, 0, 2, and 4.

Answer 1

To create an input-output table for the function \( f(x) = \frac{1}{2}x + 3 \), we will calculate the output \( f(x) \) for each input \( x \) given in the problem: -4, -3, 0, 2, and 4.

Here are the calculations:

1. **For \( x = -4 \)**:
\[
f(-4) = \frac{1}{2}(-4) + 3 = -2 + 3 = 1
\]

2. **For \( x = -3 \)**:
\[
f(-3) = \frac{1}{2}(-3) + 3 = -1.5 + 3 = 1.5
\]

3. **For \( x = 0 \)**:
\[
f(0) = \frac{1}{2}(0) + 3 = 0 + 3 = 3
\]

4. **For \( x = 2 \)**:
\[
f(2) = \frac{1}{2}(2) + 3 = 1 + 3 = 4
\]

5. **For \( x = 4 \)**:
\[
f(4) = \frac{1}{2}(4) + 3 = 2 + 3 = 5
\]

Now we can compile these results into an input-output table:

| \( x \) | \( f(x) \) |
|---------|------------|
| -4 | 1 |
| -3 | 1.5 |
| 0 | 3 |
| 2 | 4 |
| 4 | 5 |

### Summary of Results:
- \( f(-4) = 1 \)
- \( f(-3) = 1.5 \)
- \( f(0) = 3 \)
- \( f(2) = 4 \)
- \( f(4) = 5 \)

With this table, you can now visually compare the corresponding values to the graphs available to find the one that accurately represents the function \( f(x) = \frac{1}{2}x + 3 \). Look for a graph that passes through the points:
- (-4, 1)
- (-3, 1.5)
- (0, 3)
- (2, 4)
- (4, 5)

The correct graph will consistently show these values.