Question

which function represents a reflection of $f(x) = \frac{3}{8}(4)^x$ across the $y$-axis?\
$g(x) = \frac{8}{3}(4)^{-x}$\
$g(x) = -\frac{3}{8}(4)^x$\
$g(x) = \frac{3}{8}(4)^{-x}$\
$g(x) = -\frac{3}{8}\left(\frac{1}{4}\
ight)^x$

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 \(f(x)=\frac{3}{8}(4)^{x}\), when we reflect it across the \(y\) - axis, we substitute \(x\) with \(-x\) in the function. So \(g(x)=f(-x)=\frac{3}{8}(4)^{-x}\).

Answer:

\(g(x)=\frac{3}{8}(4)^{-x}\) (the third option among the given options)