Question

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

Answer 1

To complete the input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we can select various input values for \( x \) and calculate the corresponding outputs using the function.

Let's calculate some values:

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

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

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

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

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

6. For \( x = 5 \):
\[
f(5) = (5 - 2)^2 + 3 = (3)^2 + 3 = 9 + 3 = 12
\]

Now, we can summarize these computations in an input-output table:

| \( x \) | \( f(x) \) |
|-----------|--------------|
| 0 | 7 |
| 1 | 4 |
| 2 | 3 |
| 3 | 4 |
| 4 | 7 |
| 5 | 12 |

You can extend this table further by adding more input values and calculating \( f(x) \) as needed!