Question

the function $f(x) = \sqrt{x}$ is translated 4 units right to form function $g(x)$. which equation represents this transformation? $\bigcirc\\ g(x) = \sqrt{x - 4}$ $\bigcirc\\ g(x) = \sqrt{x} + 4$ $\bigcirc\\ g(x) = \sqrt{x} - 4$ $\bigcirc\\ g(x) = \sqrt{x + 4}$

Explanation:

Step1: Recall Horizontal Translation Rule

For a function \( y = f(x) \), a horizontal translation \( h \) units to the right is given by \( y = f(x - h) \).

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

Here, \( h = 4 \) (translated 4 units right). So substitute \( x \) with \( x - 4 \) in \( f(x) \).
Thus, \( g(x)=f(x - 4)=\sqrt{x - 4} \).

Answer:

\( g(x) = \sqrt{x - 4} \) (the first option: \( g(x)=\sqrt{x - 4} \))