Question

the graph of g(x) is the result of translating the graph of f(x) = 3^x six units to the right. what is the equation of g(x)?

( g(x) = 3^x - 6 )

( g(x) = 3^{x + 6} )

( g(x) = 3^{x - 6} )

( g(x) = 3^x + 6 )

Explanation:

Step1: Recall Horizontal Translation Rule

For a function \( y = f(x) \), translating it \( h \) units to the right gives \( y = f(x - h) \).

Step2: Apply the Rule to \( f(x) = 3^x \)

Here, \( h = 6 \) (translating 6 units right). So substitute \( x \) with \( x - 6 \) in \( f(x) \).
Thus, \( g(x) = f(x - 6) = 3^{x - 6} \).

Answer:

\( g(x) = 3^{x - 6} \) (the third option: \( g(x) = 3^{x - 6} \))