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) −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 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) −2 16 −1 1 0 0 1 1 2 16

Answer 1

To determine which table provides points for an even function, we need to check if \( f(x) = f(-x) \) for every value of \( x \).

An even function is symmetric with respect to the y-axis, meaning that for each \( x \), the corresponding \( f(x) \) value must match \( f(-x) \).

Let's analyze each provided table:

1. **Table 1:**
- \( x = -2, f(-2) = -8 \)
- \( x = 2, f(2) = 8 \)
- Clearly, \( -8 \neq 8 \), so this table does not represent an even function.

2. **Table 2:**
- \( x = -2, f(-2) = -1 \)
- \( x = 2, f(2) = 1 \)
- Clearly, \( -1 \neq 1 \), so this table does not represent an even function.

3. **Table 3:**
- \( x = -2, f(-2) = 1 \)
- \( x = 2, f(2) = -1 \)
- Clearly, \( 1 \neq -1 \), so this table does not represent an even function.

4. **Table 4:**
- \( x = -2, f(-2) = 16 \)
- \( x = 2, f(2) = 16 \)
- Here, \( 16 = 16 \), and we need to check more pairs:
- \( x = -1, f(-1) = 1 \)
- \( x = 1, f(1) = 1 \)
- \( 1 = 1 \)
- \( x = 0, f(0) = 0 \) (this one is symmetric by default)
- This table seems to be even so far.

The final table is not needed as we have already confirmed Table 4 to have shown even characteristics.

The table that provides points for an even function is **Table 4**:
- \( x f(x) \)
- \( -2, 16 \)
- \( -1, 1 \)
- \( 0, 0 \)
- \( 1, 1 \)
- \( 2, 16 \)

This table satisfies \( f(x) = f(-x) \) for all \( x \) values given.