Question

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