Question

f(x) = \sqrt3{x - 4} + 1; describe the transformation; options: right 4 units, up 1 unit; left 4 units, down 1 unit; left 4 units, up 1 unit; right 4 units, down 1 unit

Explanation:

Step1: Recall transformation rules

For a function \( y = \sqrt[3]{x - h}+k \), the horizontal shift is \( h \) units (right if \( h>0 \), left if \( h<0 \)) and vertical shift is \( k \) units (up if \( k>0 \), down if \( k<0 \)).

Step2: Identify \( h \) and \( k \)

In \( f(x)=\sqrt[3]{x - 4}+1 \), we have \( h = 4 \) and \( k = 1 \). So horizontal shift: right 4 units (since \( h = 4>0 \)), vertical shift: up 1 unit (since \( k = 1>0 \)).

Answer:

A. Right 4 units, up 1 unit