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

Question

x f(x)
-1
0
1
2
what's the F(x)'s

Answer 1

To create an input-output table for the function \( f(x) = (x - 2)^2 + 3 \), we need to calculate \( f(x) \) for each given value of \( x \).

Let's compute \( f(x) \) for \( x = -1, 0, 1, 2 \):

1. For \( x = -1 \): \[ f(-1) = (-1 - 2)^2 + 3 = (-3)^2 + 3 = 9 + 3 = 12 \]

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

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

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

Now, we can create the input-output table:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -1 & 12 \ 0 & 7 \ 1 & 4 \ 2 & 3 \ \hline \end{array} \]

So, the final table is:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -1 & 12 \ 0 & 7 \ 1 & 4 \ 2 & 3 \ \hline \end{array} \]