Question

6. Complete the input-output table for the function f(x) = (x−2)2+3
(2 points)
x f(x)
1 f(1)=

4 f(4)=

Answer 1

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

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

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

Now we can fill in the completed table:

| \( x \) | \( f(x) \) |
|-----------|-------------|
| 1 | 4 |
| 4 | 7 |