Using translation concepts, the function g is given as follows:
g(x) = -|x - 4| + 1
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that function g(x) is the function f(x) vertically compressed by a factor of 2, hence:
g(x) = 0.5f(x)
g(x) = 0.5(-2|x - 4| + 2)
g(x) = -|x - 4| + 1
More can be learned about translation concepts at https://brainly.com/question/4521517
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