Question

Which table provides points for an even function?(1 point)
Responses

x f(x)
−2 1
−1 2
0 0
1 −2
2 −1
x f left parenthesis x right parenthesis negative 2 1 negative 1 2 0 0 1 negative 2 2 negative 1

x f(x)
−1
−2
0 −1
1 0
2 1
3 2
x f left parenthesis x right parenthesis negative 1 negative 2 0 negative 1 1 0 2 1 3 2

x f(x)
−2 16
−1 1
0 0
1 1
2 16
x f left parenthesis x right parenthesis negative 2 16 negative 1 1 0 0 1 1 2 16

x f(x)
−2 −8
−1 −1
0 0
1 1
2 8

Answer 1

An even function is defined by the property that \( f(x) = f(-x) \) for all \( x \).

Let's check each table for this property:

1. **First Table**:
- \( f(-2) = 1 \) and \( f(2) = -1 \) → Not equal.
- \( f(-1) = 2 \) and \( f(1) = -2 \) → Not equal.
- \( f(0) = 0 \) → Equal.
- Since there are pairs that do not match, this is not an even function.

2. **Second Table**:
- \( f(-1) = -2 \) and \( f(1) = 0 \) → Not equal.
- \( f(0) = -1 \) → Not equal to itself when looking at the opposite side.
- Since there are pairs that do not match, this is not an even function.

3. **Third Table**:
- \( f(-2) = 16 \) and \( f(2) = 16 \) → Equal.
- \( f(-1) = 1 \) and \( f(1) = 1 \) → Equal.
- \( f(0) = 0 \) → Equal.
- All values match their negatives, so this is an even function.

4. **Fourth Table**:
- \( f(-2) = -8 \) and \( f(2) = 8 \) → Not equal.
- \( f(-1) = -1 \) and \( f(1) = 1 \) → Not equal.
- \( f(0) = 0 \) → Equal.
- Since there are pairs that do not match, this is not an even function.

The correct answer is the **third table**:

\[
\begin{align*}
x & f(x) \\
-2 & 16 \\
-1 & 1 \\
0 & 0 \\
1 & 1 \\
2 & 16 \\
\end{align*}
\]