Question

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

A. g(x) = -3/8(1/4)x

B. g(x) = -3/8 (4)x

C. g(x) = 8/3 (4)-x

D. g(x) = 3/8 (4)–x

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)=((3)/(8))(4^x)`, replacing x with -x, we get

`g(x)=((3)/(8))(4^(-x))`

answer is D

Answer 2

D is correct option.
`g(x)=(3)/(8)\cdot (4)^(-x)`

Explanation:

We are given a function
`f(x)=(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)=(3)/(8)\cdot (4)^(-x)`

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

`g(x)=(3)/(8)\cdot (4)^(-x)`

Thus, D is correct option.