Question

G(x)= -log₂(x + 4) - 1. What are the coordinates of the reference points of the transformation

Answer 1

The coordinates of the reference points of the transformation are (-3, -1).

Step-by-step explanation:

The function g(x) = -log₂(x + 4) - 1 represents a logarithmic transformation.

The reference points of the transformation are the points where the base of the logarithm becomes 1.

1. To find the x-coordinate of the reference points, set the base of the logarithm equal to 1 and solve for x: 2(x + 4) = 1.
2. The value of x that satisfies this equation is x = -3.
3. The y-coordinate (f(x)) of the reference points can be found by substituting x = -3 into the original function: g(-3) = -log₂(-3 + 4) - 1 = -log₂1 - 1 = -0 - 1 = -1.

Therefore, the coordinates of the reference point of the transformation are (-3, -1).