Question

Which table shows that y=−f(x)
results in a reflection over the x-axis?

(1 point)
Responses

x −f(x)
2 0
3 1
6 2
x f left parenthesis x right parenthesis 2 0 3 1 6 2

x −f(x)
−2
0
−3
−1
−6
−2
x f left parenthesis x right parenthesis negative 2 0 negative 3 negative 1 negative 6 negative 2

x −f(x)
−2
0
−3
1
−6
2
x f left parenthesis x right parenthesis negative 2 0 negative 3 1 negative 6 2

x −f(x)
2 0
3 −1
6 −2
x f left parenthesis x right parenthesis 2 0 3 negative 1 6 negative 2
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Answer 1

To determine which table indicates that \( y = -f(x) \) represents a reflection over the x-axis, we need to examine how the values of \( f(x) \) and \( -f(x) \) correspond to each other in each table.

1. **Table 1**
- \( f(x) \): \( 2, 0, 3, 1, 6, 2 \)
- \( -f(x) \): \( 0, -1, -2 \)

Here, there are mismatches in the entries.

2. **Table 2**
- \( f(x) \): \( -2, 0, -3, -1, -6, -2 \)
- \( -f(x) \): \( 2, 0, 3, 1, 6, 2 \)

This shows that \( -f(x) \) is the negation of \( f(x) \), which confirms a reflection over the x-axis.

3. **Table 3**
- \( f(x) \): \( -2, 0, -3, 1, -6, 2 \)
- \( -f(x) \): \( 2, 0, 3, -1, 6, -2 \)

Again, this shows matches for some values but does not consistently show that it is a strict negation.

4. **Table 4**
- \( f(x) \): \( 2, 0, 3, -1, 6, -2 \)
- \( -f(x) \): \( 0, -1, -2 \)

Similarly, there are mismatches here.

Upon examination, **Table 2** is the only table where \( -f(x) \) values are exactly the negations of \( f(x) \) values, indicating a consistent reflection over the x-axis.

Thus, **Table 2** corresponds to \( y = -f(x) \).