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

You can think of reflections as rotations of 180 degrees about the specified axis. Thus reflecting any function y = f(x), not just an exponential: About the y-axis, keeps y the same but flips the sign of x to -x. so y = f(-x) is the reflected function. About the x-axis, keeps x the same but flips the sign of y to -y so -y = f(x) or y = - f(x). So in your example of reflecting f(x) = 4x about the y-axis:y = 4(-x) = - 4x

Answer Link

erinna erinna · Answer 2 · 2019-07-18T13:32:50+02:00

Answer:

The function [tex]g(x)=\frac{3}{8}(4)^{-x}[/tex] represents a reflection of [tex]f(x)=\frac{3}{8}(4)^{x}[/tex] across the y-axis.

Step-by-step explanation:

The given function is

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

If a function reflected across the y-axis then the sign of x-coordinate is changed but the y-coordinate remain the same.

Mathematically it can be defined as

[tex](x,y)\rightarrow (-x,y)[/tex]

Let function g(x) represents a reflection of f(x) across the y-axis. So, the required function is

[tex]g(x)=f(-x)[/tex]

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

Therefore the function [tex]g(x)=\frac{3}{8}(4)^{-x}[/tex] represents a reflection of [tex]f(x)=\frac{3}{8}(4)^{x}[/tex] across the y-axis.