Describe how the function g(x)=1/2|x-4| transforms the function f(x)=|x-4|

Answer 1

The function g(x) = 1/2|x-4| is a transformation of the function f(x) = |x-4|.

The transformation involves scaling the graph of f(x) vertically by a factor of 1/2. This means that every point on the graph of f(x) is halved in its y-coordinate on the graph of g(x).

In addition to the vertical scaling, the graph of g(x) is also shifted upwards or downwards depending on the sign inside the absolute value. In this case, the shifting occurs horizontally and is a translation of 4 units to the left. This is because g(x) = f(x-4), meaning that each x-value on the graph of g(x) is shifted left by 4 units compared to the graph of f(x).

Therefore, the transformation of f(x) = |x-4| to g(x) = 1/2|x-4| involves a vertical scaling by 1/2 and a horizontal shifting left by 4 units.