Question

Complete the input-output table for the function f(x)=(x-2)^2+3.
| x | f(x) |
|---|---|
| 1 | f(1)=4 |
| 2 | f(2)=\square |
| 3 | f(3)=4 |
| 4 | f(4)=\square |

Answer 1

To complete the input-output table for the function \( f(x) = (x-2)^2 + 3 \), we'll calculate \( f(2) \) and \( f(4) \).

1. **Calculating \( f(2) \)**:
\[
f(2) = (2-2)^2 + 3 = 0^2 + 3 = 0 + 3 = 3
\]

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

Now we can fill in the table:

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

So, the completed table is:

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