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

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erinna erinna · Answer 2 · 2019-07-18T07:32:50-04:00

Answer:

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

Step-by-step explanation:

The given function is

\(f(x)=\frac{3}{8}(4)^{x}\)

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

\((x,y)\rightarrow (-x,y)\)

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

\(g(x)=f(-x)\)

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

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