Question

question the graph of $f(x) = 2\sqrt{x}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ right 4 units.

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), shifting it right by \( h \) units gives \( y = f(x - h) \).

Step2: Apply shift to \( f(x) \)

Given \( f(x)=2\sqrt{x} \), shift right 4 units. So replace \( x \) with \( x - 4 \) in \( f(x) \).
Thus, \( g(x)=2\sqrt{x - 4} \).

Answer:

\( g(x) = 2\sqrt{x - 4} \)