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

Question

.(2 points)
x f(x)
1 f(1)=
2 f(2)=
3 f(3)=
4 f(4)=

Answer 1

To complete the input-output table using the function \( f(x) = (x - 2)^2 + 3 \), we will calculate \( f(x) \) for each provided \( x \) value.

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

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

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

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

Now we can complete the table:

| x | f(x) | |---|------| | 1 | 4 | | 2 | 3 | | 3 | 4 | | 4 | 7 |