Question

Which answer describes the transformation of g(x)=log2(x−2) 4 from the parent function f(x)=log2x ?

Answer 1

The transformation of the function g(x)=log2(x−2) 4 from the parent function f(x)=log2x involves a vertical shift upward by 4 units.

Step-by-step explanation:

The transformation of the function g(x) = log2(x-2) + 4 from the parent function f(x) = log2x involves a vertical shift upward by 4 units.

1. The parent function f(x) = log2x has a y-intercept at (1, 0) and its graph passes through (2, 1).
2. To transform the function horizontally, we replace x with x-2.
3. To transform the function vertically, we add 4 to the result of the previous step, giving us g(x) = log2(x-2) + 4.

The graph of g(x) will be shifted upward by 4 units compared to the graph of f(x).

Answer 2

The transformation of the function g(x) = log2(x-2) from the parent function f(x) = log2x involves shifting the graph horizontally 2 units to the right.

Step-by-step explanation:

The transformation of the function g(x) = log2(x-2) from the parent function f(x) = log2x involves shifting the graph horizontally 2 units to the right. This is because the parent function has the form log2x, which corresponds to a vertical line passing through the point (1, 0) on the graph. When we replace x with x-2 in the function, we are shifting the entire graph 2 units to the right.