Question

question the graph of $f(x) = \sqrt{x}$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ right 3 units.

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), shifting it right by \( h \) units gives \( y = f(x - h) \). Here, \( h = 3 \).

Step2: Apply shift to \( f(x)=\sqrt{x} \)

Substitute \( x \) with \( x - 3 \) in \( f(x) \). So \( g(x)=f(x - 3)=\sqrt{x - 3} \).

Answer:

\( g(x)=\sqrt{x - 3} \)