The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.
What transformation must be applied to modify the absolute value function?
In this problem we find a resulting expression, that is, the function g(x) = - |x| + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.
After a quick inspection, we find that two rigid transformations were used in the following order:
- Reflection around the x-axis.
- Translation 2 units up.
Now we proceed prove this procedure:
f(x) = |x|
Step 1
f'(x) = - |x|
Step 2
g(x) = - |x| + 2
To learn more on rigid transformations: https://brainly.com/question/28004150
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