Complete the input-output table for the function f(x)=x2−x

Question

.(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 calculate \( f(x) \) for each given 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 fill in the table:

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

So the completed input-output table is:

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