Question

Which function represents a reflection of f(x) = 3/8 (4)x across the y-axis?

Answer 1

to reflect f(x) across the y axis, replace every x with -x

in other words, f(-x) is f(x) reflected across the y axis

so for $f(x)=(\frac{3}{8})(4^x)$, replacing x with -x, we get

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

answer is D

Answer 2

Answer:

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

Step-by-step explanation:

We are given a function $f(x)=\frac{3}{8}\cdot (4)^x$

We need to find new function reflection of f(x) across the y-axis.

When function reflection across y-axis $x\rightarrow -x$

$\text{Reflection across y-axis}f(x)\rightarrow f(-x)$

Therefore, $f(-x)=\frac{3}{8}\cdot (4)^{-x}$

New function, $g(x)=f(-x)$

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

Thus, D is correct option.