Question

the function $g(x) = 8(4^x)$ is reflected across the $x$-axis to create $f(x)$. what is the equation of $f(x)$? options: $f(x) = -8(4)^x$, $f(x) = -8\left(\frac{1}{4}\
ight)^x$, $f(x) = 8\left(\frac{1}{4}\
ight)^x$, $f(x) = 8(4)^x$

Explanation:

Step1: Recall reflection rule

Reflecting a function \( y = g(x) \) across the \( x \)-axis changes the sign of the function, so \( f(x)= -g(x) \).

Step2: Apply to given function

Given \( g(x)=8(4^x) \), then \( f(x)= -g(x)= -8(4^x) \).

Answer:

\( f(x) = -8(4)^x \)