Complete the input-output table for the function f(x)=(x−2)^2+3

Question

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Drag and drop each number. Match the fuction with the correct answer.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

1 Response area

2 Response area
3 Response area

4 Response area

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Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we will calculate the output for different values of \( x \).

Let's select some input values and compute the corresponding outputs:

1. For \( x = 0 \): \[ f(0) = (0 - 2)^2 + 3 = 4 + 3 = 7 \]

2. For \( x = 1 \): \[ f(1) = (1 - 2)^2 + 3 = 1 + 3 = 4 \]

3. For \( x = 2 \): \[ f(2) = (2 - 2)^2 + 3 = 0 + 3 = 3 \]

4. For \( x = 3 \): \[ f(3) = (3 - 2)^2 + 3 = 1 + 3 = 4 \]

5. For \( x = 4 \): \[ f(4) = (4 - 2)^2 + 3 = 4 + 3 = 7 \]

You can summarize the values in the input-output table:

• \( f(0) = 7 \)
• \( f(1) = 4 \)
• \( f(2) = 3 \)
• \( f(3) = 4 \)
• \( f(4) = 7 \)

Now, take the responses calculated for each input and match them with the respective response areas in your input-output table.

If your response areas are as follows:

1. Input: \( 0 \) → Output: \( 7 \)
2. Input: \( 1 \) → Output: \( 4 \)
3. Input: \( 2 \) → Output: \( 3 \)
4. Input: \( 3 \) → Output: \( 4 \)
5. Input: \( 4 \) → Output: \( 7 \)

You can assign:

• Area 1: \( 7 \)
• Area 2: \( 4 \)
• Area 3: \( 3 \)
• Area 4: \( 4 \)
• (You will also end up with a repeat for \( 4 \) and \( 7 \) if you're using common input/output values.)

Please adjust according to the area's requirement since I didn’t see the actual response area numbers.