Question

Which function represents g(x), a reflection of f(x) =1/2(3)x across the y-axis?

Answer 1

g(x) = (1/2)3^-x reflection over y axis yields (-x,y)

Answer 2

The required function -
`g(x)=(1)/(2)(3)^(-x)`

Explanation:

Given : Function represents g(x), a reflection of
`f(x) =(1)/(2)(3)^x` across the y-axis

To find : Which function represents the g(x)?

Solution :

The function
`f(x) =(1)/(2)(3)^x`

The function f(x) reflected across y-axis to form g(x)

The reflection of the point (x,y) across the y-axis is the point (-x,y).

f(x,y)→f(-x,y) , the graph of f(x) is reflected across y-axis.

Let
`y=(1)/(2)(3)^x`

After reflection across y-axis is

`g(x)=(1)/(2)(3)^(-x)`

The required function.

Refer the attached graph below.