Using translation concepts, the function g(x) is defined as follows:
g(x) = -f(x) - 8.
Since f(x) = |x|: g(x) = -|x| - 8.
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.
For this problem, the changes are given as follows:
- Reflection over the x-axis: g(x) = -f(x).
- Shift of 8 units down, hence: g(x) = -f(x) - 8;
Since f(x) = |x|: g(x) = -|x| - 8.
More can be learned about translation concepts at https://brainly.com/question/28373831
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