contestada

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

Respuesta :

apologiabiology

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 [tex]f(x)=(\frac{3}{8})(4^x)[/tex], replacing x with -x, we get

[tex]g(x)=(\frac{3}{8})(4^{-x})[/tex]

answer is D

isyllus

Answer:

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

Step-by-step explanation:

We are given a function [tex]f(x)=\frac{3}{8}\cdot (4)^x[/tex]

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

When function reflection across y-axis [tex]x\rightarrow -x[/tex]

[tex]\text{Reflection across y-axis}f(x)\rightarrow f(-x)[/tex]

Therefore, [tex]f(-x)=\frac{3}{8}\cdot (4)^{-x}[/tex]

New function, [tex]g(x)=f(-x)[/tex]

[tex]g(x)=\frac{3}{8}\cdot (4)^{-x}[/tex]

Thus, D is correct option.


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