Question

Which table shows the results of the reflection of the function over the x-axis
On graph (-2,2),(-3,3),(-1,3),(-4,4),(-5,5),(-6,6), (0,4),(1,5),(2,6)
Table 1
x y
-4 4
-3 3
-2 2
-1 3
0 4
1 5
Table 2
x y
-4 -4
-3 -3
-2 -2
-1 -3
0 -4
1 -5
Table 3
x y
4 -4
3 -3
2 -2
1 -3
0 -4
-1 -5
Table 4
x y
4 4
3 3
2 2
1 3
0 4
-1 5

Answer 1

To reflect a set of points over the x-axis, the y-coordinates of each point must be inverted (i.e., multiplied by -1), while the x-coordinates remain unchanged.

Given the original points:
- (-2, 2)
- (-3, 3)
- (-1, 3)
- (-4, 4)
- (-5, 5)
- (-6, 6)
- (0, 4)
- (1, 5)
- (2, 6)

Applying the reflection over the x-axis, we will calculate the new points:
- (-2, 2) → (-2, -2)
- (-3, 3) → (-3, -3)
- (-1, 3) → (-1, -3)
- (-4, 4) → (-4, -4)
- (-5, 5) → (-5, -5)
- (-6, 6) → (-6, -6)
- (0, 4) → (0, -4)
- (1, 5) → (1, -5)
- (2, 6) → (2, -6)

Now, let's check the tables:

- **Table 1**:
```
x y
-4 4
-3 3
-2 2
-1 3
0 4
1 5
```
(This table does not show reflected values.)

- **Table 2**:
```
x y
-4 -4
-3 -3
-2 -2
-1 -3
0 -4
1 -5
```
(This table shows the correct reflected values for points -4, -3, -2, -1, and 0, but does not include all original values or their reflected pairs.)

- **Table 3**:
```
x y
4 -4
3 -3
2 -2
1 -3
0 -4
-1 -5
```
(This table shows values that do not correspond to the reflection of the original points correctly.)

- **Table 4**:
```
x y
4 4
3 3
2 2
1 3
0 4
-1 5
```
(This table does not show reflected values.)

Based on the calculation above, **none of the provided tables accurately represent the reflection of the original points over the x-axis.** However, Table 2 closely resembles some of the reflected values.