Question

which function represents g(x), a reflection of f(x) = \frac{1}{2}(3)^x across the y-axis?\
\bigcirc\\ g(x) = 2(3)^x\
\bigcirc\\ g(x) = -\frac{1}{2}(3)^x\
\bigcirc\\ g(x) = \frac{1}{2}(3)^{-x}\
\bigcirc\\ g(x) = 2(3)^{-x}

Explanation:

Step1: Recall reflection over y - axis rule

The rule for reflecting a function \(y = f(x)\) across the \(y\) - axis is \(y=f(-x)\).

Step2: Apply the rule to the given function

Given the function \(f(x)=\frac{1}{2}(3)^{x}\), when we reflect it across the \(y\) - axis, we substitute \(x\) with \(-x\) in the function. So \(g(x)=f(-x)=\frac{1}{2}(3)^{-x}\).

Answer:

\(g(x)=\frac{1}{2}(3)^{-x}\) (corresponding to the option \(g(x)=\frac{1}{2}(3)^{-x}\))