Question

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 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:

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