Question

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

x f(x)
−2
−8
−1
−1
0 0
1 1
2 8
x f left parenthesis x right parenthesis negative 2 negative 8 negative 1 negative 1 0 0 1 1 2 8

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

Answer 1

An even function satisfies the condition \( f(x) = f(-x) \) for all \( x \). This means that the values of the function at \( x \) and \( -x \) must be equal.

Let's examine the given tables to see which one represents an even function:

1. **Table 1**:
- \( f(-2) = -8 \), \( f(2) = 8 \) (not equal)
- \( f(-1) = -1 \), \( f(1) = 1 \) (not equal)
- \( f(0) = 0 \)

This table is not even.

2. **Table 2**:
- \( f(-2) = 1 \), \( f(2) = -1 \) (not equal)
- \( f(-1) = 2 \), \( f(1) = -2 \) (not equal)
- \( f(0) = 0 \)

This table is not even.

3. **Table 3**:
- \( f(-1) = -2 \), \( f(1) = 0 \) (not equal)
- \( f(0) = -1 \)
- \( f(2) = 1 \) and no corresponding negative for 2 in table.

This table is not even.

4. **Table 4**:
- \( f(-2) = 16 \), \( f(2) = 16 \) (equal)
- \( f(-1) = 1 \), \( f(1) = 1 \) (equal)
- \( f(0) = 0 \)

This table satisfies the condition for evenness, as the function values match for all corresponding negative and positive inputs.

Therefore, the table which provides points for an even function is **Table 4**.