Question

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

Answer 1

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 2

The function
`g(x)=(3)/(8)(4)^(-x)` represents a reflection of
`f(x)=(3)/(8)(4)^(x)` across the y-axis.

Explanation:

The given function is

`f(x)=(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)=(3)/(8)(4)^(-x)`
`[\because f(x)=(3)/(8)(4)^(x)]`

Therefore the function
`g(x)=(3)/(8)(4)^(-x)` represents a reflection of
`f(x)=(3)/(8)(4)^(x)` across the y-axis.