Complete the input-output table for the function f(x)=x2−x .(2 points) x f(x) −2 −1 2 0 0 1 2 2

Answer 1

To complete the input-output table for the function \( f(x) = x^2 - x \), we will evaluate the function at each specified value of \( x \).

1. For \( x = -2 \): \[ f(-2) = (-2)^2 - (-2) = 4 + 2 = 6 \]

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

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

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

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

6. For \( x = 2 \) (again): \[ f(2) = (2)^2 - (2) = 4 - 2 = 2 \]

Now we can summarize the values in the input-output table:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline -2 & 6 \ -1 & 2 \ 0 & 0 \ 1 & 0 \ 2 & 2 \ 2 & 2 \ \hline \end{array} \]

Thus, the completed table is:

| x | f(x) | |----|------| | -2 | 6 | | -1 | 2 | | 0 | 0 | | 1 | 0 | | 2 | 2 | | 2 | 2 |