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

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

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

Answer

Answer:

D. $g(x)=\frac{3}{8}(4)^{-x}$

Explanation:

Step1: Recall reflection rule

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

Step2: Apply rule to given function

Given $f(x)=\frac{3}{8}(4)^{x}$, then $g(x)=f(-x)=\frac{3}{8}(4)^{-x}$.