Question

Which table shows the reflection of f(x) across the x-axis?

The first picture is the given table and the other three are the possible answers.

Answer 1

The correct option is;

x, f(x)

-5, 3

-1, -2

2, -4

6, 1

Explanation:

The reflection of a point (x, y) across the x-axis is given by the relation;

Coordinate of the pre-image (x, y)
`\overset{Reflection \ across \ the \ x-axis}{\rightarrow}` Coordinate of image (x, -y)

Therefore, we have for the points as follows;

(-5, -3)
`\overset{Reflection \ across \ the \ x-axis}{\rightarrow}` (-5, 3)

`(-5, -3) \mapsto (-5, 3)`

(-1, 2)
`\overset{Reflection \ across \ the \ x-axis}{\rightarrow}` (-1, -2)

`(-1, 2) \mapsto (-1, -2)`

(2, 4)
`\overset{Reflection \ across \ the \ x-axis}{\rightarrow}` (2, -4)

`(2, 4) \mapsto (2, -4)`

(6, -1)
`\overset{Reflection \ across \ the \ x-axis}{\rightarrow}` (6, 1)

`(6, -1) \mapsto (6, 1)`