Use input-output tables to determine which graph accurately represents the function f(x) = ½ x + 3 with inputs of -4, -2, 0, 2, and 4. (1 point)

Question

-5-
-4-
3.
5432
2.
-1
0 1 23 45 6
O +0.
0
--1-
--2-
--3-
--4-
-5+
-3-
2-
-1-
01
-3 2
0
1
2
3 4
6-
-5-
-2-
-3-
4-
30
-2-
1
-0.
-3 -2
-1 0
1
2
3
4
1
-2
3.
6-
-5-
4-
3
-2-
1-
0
-4 -3 -2 -1
0 1
2 3 4

Answer 1

We need to use the function \( f(x) = \frac{1}{2}x + 3 \) to find the outputs for the given inputs: \( -4, -2, 0, 2, \) and \( 4 \).

Let's calculate the outputs for each input step by step:

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

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

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

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

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

Now we can summarize the results in an input-output table:

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

Now, we should look for a graph that contains the points:

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

From the graphs you provided, we will determine which one accurately represents these points:

1. First graph: Check if it goes through the points listed.
2. Second graph: Check similarly.
3. Third graph: Do the same.
4. Fourth graph: Do the same.

The accurate graph will be the one that passes through all the calculated points, so proceed to compare them against the provided graphs. Since I cannot see the graphs, I suggest inspecting each one against the calculated points. The correct graph will contain all five points and maintain the linearity of the function. If you need help with interpreting what the graphs look like based on the points, please provide a description or the images themselves.