Use the image to answer the question.

Question

A graphed function starting on the x axis has an arrow at the other end passes through three points on a coordinate plane. The x-axis ranges from negative 9 to 9 in unit increments and the y-axis ranges from negative 11 to 11 in unit increments.

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 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 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

Answer 1

To determine which table shows that \( y = -f(x) \) results in a reflection over the x-axis, we need to look for values of \( -f(x) \) that are the negative of the corresponding values of \( f(x) \).

Let's analyze the provided options:

1. First option:

   • x: -2, 0, -3, 1, -6, 2
   • -f(x): The table doesn't provide values of \( f(x) \).

2. Second option:

   • x: 2, 0, 3, 1, 6, 2
   • -f(x): Again, we don't have values of \( f(x) \) provided.

3. Third option:

   • x: -2, 0, -3, -1, -6, -2
   • -f(x): -2, 0, -3, -1, -6, -2
   • Here, \( -f(-2) = -(-2) = 2 \), \( -f(0) = -(0) = 0 \), etc. However, we need the original function values \( f(x) \) to verify this.

4. Fourth option:

   • x: 2, 0, 3, 6
   • -f(x): 0, -1, -2
   • Similar to the other options, we need the original function values.

Since we need a reflection across the x-axis, we are looking for a table where the output of -f(x) is exactly the negative of f(x). However, without the original values f(x) listed, we can't make an accurate determination.

To give you an answer based on the format, it seems that the third option is formatted correctly since each value of -f(x) represents potential negative counterparts of original function outputs.

If we assume standard values of f(x) would result in y values that are the numerical opposites, the third option seems to reflect this property about the x-axis.

So the best choice based on the reflection definition is:

Third option:

• \( x: -2, 0, -3, -1, -6, -2 \)
• \( -f(x): -2, 0, -3, -1, -6, -2 \)

Conclusion: The third option shows that \( -f(x) \) reflects over the x-axis, assuming standard function values.