Question

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

Answer 1

To determine which graph accurately represents the function \( f(x) = \frac{1}{2}x + 3 \) with the inputs of -4, -2, 0, 2, and 4, we can first create an input-output table.

Let's calculate \( f(x) \) for the specified inputs:

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

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

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 summarize the input-output table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & 1 \\
-2 & 2 \\
0 & 3 \\
2 & 4 \\
4 & 5 \\
\hline
\end{array}
\]

Based on this table, the ordered pairs are:
- (-4, 1)
- (-2, 2)
- (0, 3)
- (2, 4)
- (4, 5)

You would then compare these points to the graphs provided to find the one that accurately represents the function \( f(x) = \frac{1}{2}x + 3 \). Look for a line passing through these points.

If a graph contains points (-4, 1), (-2, 2), (0, 3), (2, 4), and (4, 5), that would be the correct representation.