Question

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

2,0
3,-1
6,-2

-2,0
-3,-1
-6,-2

-2,0
-3,1
-6,2


2,0
3,1
6,2

Answer 1

To determine which table shows the results of the function \( y = -f(x) \), which represents a reflection of the function \( f(x) \) over the x-axis, we need to take the values of \( f(x) \) in each given table and negate them (multiply them by -1).

Let's first assume each original table represents the values of \( f(x) \) and then apply the transformation to see which reflects over the x-axis:

1. Original values:
- \( f(2) = 0 \) → \( y = -f(2) = 0 \)
- \( f(3) = -1 \) → \( y = -f(3) = 1 \)
- \( f(6) = -2 \) → \( y = -f(6) = 2 \)

Results: \((2, 0), (3, 1), (6, 2)\)

2. Original values:
- \( f(-2) = 0 \) → \( y = -f(-2) = 0 \)
- \( f(-3) = -1 \) → \( y = -f(-3) = 1 \)
- \( f(-6) = -2 \) → \( y = -f(-6) = 2 \)

Results: \((-2, 0), (-3, 1), (-6, 2)\)

3. Original values:
- \( f(-2) = 0 \) → \( y = -f(-2) = 0 \)
- \( f(-3) = 1 \) → \( y = -f(-3) = -1 \)
- \( f(-6) = 2 \) → \( y = -f(-6) = -2 \)

Results: \((-2, 0), (-3, -1), (-6, -2)\)

4. Original values:
- \( f(2) = 0 \) → \( y = -f(2) = 0 \)
- \( f(3) = 1 \) → \( y = -f(3) = -1 \)
- \( f(6) = 2 \) → \( y = -f(6) = -2 \)

Results: \((2, 0), (3, -1), (6, -2)\)

Now, let's summarize the transformations with respect to \( f(x) \):

- The results of \( y = -f(x) \) are as follows:
- \( (2, 0) \)
- \( (3, 1) \)
- \( (6, 2) \)

From the tables provided, the one that matches these results is:

**Option 3:** \((-2, 0), (-3, 1), (-6, 2)\)

So, the correct table showing the results of \( y = -f(x) \) (reflection over the x-axis) is:

**\((-2, 0), (-3, 1), (-6, 2)\)**.