Answer:
The final function is [tex]g(x)=\dfrac{1}{2}(x+2)^5-1[/tex]
A is correct
Step-by-step explanation:
Given: Parent function [tex]f(x)=x^5[/tex]
We need to apply sequence of transformation.
Step 1: Compress vertically by 1/2
If function compress vertically number multiply by factor
[tex]f(x)=\dfrac{1}{2}x^5[/tex]
Step 2: Shift 2 unit left
For left and right shift change in horizontal.
For a unit change , x-> x+a
[tex]f(x)=\dfrac{1}{2}(x+2)^5[/tex]
Step 3: Shift 1 unit down
For up and down change in y value or vertically shift.
For down subtract 1 unit from function
[tex]f(x)=\dfrac{1}{2}(x+2)^5-1[/tex]
Please see the attachment for transformation step by step.
Hence, The final function is [tex]f(x)=\dfrac{1}{2}(x+2)^5-1[/tex]
