Which function results after applying the sequence of transformations to f(x)=x^5Compress vertically by 1/2Shift left 2 unitsShift down 1 unit

Accepted Solution

Answer:The final function is [tex]g(x)=\dfrac{1}{2}(x+2)^5-1[/tex]A is correctStep-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 downFor 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]