Questions: Question 15 5 pts For the function y=2x+6 find the original point and the reflection about the x -axis for the value x=-1 (A) a(1,4) and (1,-4) (C) o (-1,4) and (-1,-4) (D) (0,4) and (0,-4)

Question 15
5 pts

For the function y=2x+6 find the original point and the reflection about the x -axis for the value x=-1
(A) a(1,4) and (1,-4)
(C) o (-1,4) and (-1,-4)
(D) (0,4) and (0,-4)

Transcript text: Question 15 5 pts For the function $y=2 x+6$ find the original point and the reflection about the x -axis for the value $x=-1$ (A) $\mathrm{a}(1,4)$ and $(1,-4)$ (C) o $(-1,4)$ and ( $-1,-4)$ (D) $(0,4)$ and $(0,-4)$

Solution

Solution Steps

To solve this problem, we need to find the value of the function $ y = 2x + 6 $ at $ x = -1 $. This will give us the original point. Then, to find the reflection of this point about the x-axis, we will negate the y-coordinate of the original point.

Step 1: Find the Original Point

To find the original point for $ x = -1 $, we substitute $ x $ into the function $ y = 2x + 6 $:

\[ y = 2(-1) + 6 = -2 + 6 = 4 \]

Thus, the original point is $ (-1, 4) $.

Step 2: Find the Reflection About the X-Axis

The reflection of a point $ (x, y) $ about the x-axis is given by $ (x, -y) $. Therefore, for the original point $ (-1, 4) $:

\[ \text{Reflected Point} = (-1, -4) \]