Question

Which function represents g(x), a reflection of f(x) = 6(1/3)^x across the y-axis?

Answer 1

The function that represents the reflection of f(x) = 6(1/3)^x across the y-axis is g(x) = 6(1/3)^{-x}.

Step-by-step explanation:

In order to find the function that represents the reflection of f(x) = 6(1/3)^x across the y-axis, we need to change the sign of the x-values.

When graph of f(x) reflects across y axis then f(x) becomes f(-x)

The general form of a reflection across the y-axis is g(x) = f(-x).

So, substituting -x in place of x in the original function, we get g(x) = 6(1/3)^{-x}.

Thus the function that represents the reflection of f(x) across the y-axis is g(x) = 6(1/3)^{-x}.

Answer 2

g(x)=
`6((1)/(3))^(-x)`

Step-by-step explanation:

a reflection of f(x) = 6(1/3)^x across the y-axis

Given f(x)=
`6((1)/(3))^x`

When graph of f(x) reflects across y axis then f(x) becomes f(-x)

For reflection across y axis we replace x with -x

f(x)=
`6((1)/(3))^x`

f(-x)=
`6((1)/(3))^(-x)`

f(-x) is a reflection across the y axis that is our g(x)

So g(x)=
`6((1)/(3))^(-x)`