Question

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

Answer 1

To determine which graph accurately represents the function \( f(x) = \frac{1}{2}x + 3 \) using input-output tables, we first need to calculate the output values (f(x)) for the given inputs: −4, −2, 0, 2, and 4.

We will compute:

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 results in a table:

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

Now we have the following points:

- \( (-4, 1) \)
- \( (-2, 2) \)
- \( (0, 3) \)
- \( (2, 4) \)
- \( (4, 5) \)

To identify the correct graph, look for a graph that includes these points. The graph should be a straight line, as the function \( f(x) = \frac{1}{2}x + 3 \) is linear.

If you have multiple graph options, find the one that passes through all these specified points, and that will be the correct graph representing the function.