Using translation concepts, it is found that:
- The parent function y = [tex]0.5^x[/tex] is decreasing across it's domain because it's base, b, is such that 0 < |b| < 1.
- The function f shifts the parent function 8 units up.
- The function f shifts the parent function 5 units right.
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]y = 0.5^x[/tex]
It has a base with absolute value between 0 and 1, hence it is decreasing.
The changes to the function are given as follows:
- y -> y + 8, hence the function was shifted 8 units up.
- x -> x - 5, hence the function was shifted 5 units right.
More can be learned about translation concepts at https://brainly.com/question/4521517
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