Using translation concepts, it is found that the resulting function is given by: [tex]f(x) = -3(x - 1)^5 + 2[/tex].
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.
In this problem, the function is:
[tex]f(x) = x^5[/tex]
The transformations are as follows:
- Stretch vertically by a factor of 3, hence [tex]f(x) = 3x^5[/tex].
- Reflect across the x-axis, hence [tex]f(x) = -3x^5[/tex]
- Shift right 1 unit, hence [tex]f(x) = -3(x - 1)^5[/tex].
- Shift up 2 units, hence [tex]f(x) = -3(x - 1)^5 + 2[/tex].
More can be learned about translation concepts at https://brainly.com/question/4521517
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