Question

Which table provides points for an even function
Table 1
x f(x)
-2 8
-1 5
0 4
1 -5
2 -8
Table 2
x f(x)
-2 -2
-1 -1
0 0
1 1
2 2
Table 3
x f(x)
-2 8
-1 5
0 4
1 5
2 8
Table 4
x f(x)
-1 -2
0 -1
1 0
2 1
3 2

Answer 1

An even function is defined by the property that \( f(-x) = f(x) \) for all \( x \) in the function's domain. This means that the function has symmetrical values about the y-axis.

Now, let's analyze each table to determine if the function is even:

### Table 1
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-2 & 8 \\
-1 & 5 \\
0 & 4 \\
1 & -5 \\
2 & -8 \\
\end{array}
\]
- \( f(-2) = 8 \) and \( f(2) = -8 \) (not equal)
- \( f(-1) = 5 \) and \( f(1) = -5 \) (not equal)
- **Not an even function.**

### Table 2
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-2 & -2 \\
-1 & -1 \\
0 & 0 \\
1 & 1 \\
2 & 2 \\
\end{array}
\]
- \( f(-2) = -2 \) and \( f(2) = 2 \) (not equal)
- \( f(-1) = -1 \) and \( f(1) = 1 \) (not equal)
- **Not an even function.**

### Table 3
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-2 & 8 \\
-1 & 5 \\
0 & 4 \\
1 & 5 \\
2 & 8 \\
\end{array}
\]
- \( f(-2) = 8 \) and \( f(2) = 8 \) (equal)
- \( f(-1) = 5 \) and \( f(1) = 5 \) (equal)
- \( f(0) = 4 \) (symmetric around 0)
- **This is an even function.**

### Table 4
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-1 & -2 \\
0 & -1 \\
1 & 0 \\
2 & 1 \\
3 & 2 \\
\end{array}
\]
- \( f(-1) = -2 \) and \( f(1) = 0 \) (not equal)
- \( f(0) = -1 \) (not symmetric for negative values)
- **Not an even function.**

Based on the evaluations, **Table 3** provides points for an even function.