Question

The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?

Answer 1

`(-3,4/375)`

Explanation:

Given

`f(x) = (1)/(6)((2)/(5))^x`

Reflection: Across y-axis

Required

The ordered pair on g(x)

The rule of reflection across y-axis is:

`(x,y) = (-x,y)`

So, we have:

`g(x) = f(-x)`

f(-x) is:

`f(-x) = (1)/(6)((2)/(5))^{-x`

Recall that:

`g(x) = f(-x)`

Hence:

`g(x) = (1)/(6)((2)/(5))^{-x`

From the options (missing in the question), the ordered pair is:

`(-3,4/375)`

To check this, we have:

`g(x) = (1)/(6)((2)/(5))^{-x`

`g(-3) = (1)/(6)((2)/(5))^{--3`

`g(-3) = (1)/(6)((2)/(5))^{3`

Expand

`g(-3) = (1)/(6)((8)/(125))`

Simplify

`g(-3) = (1)/(3)((4)/(125))`

Open bracket

`g(-3) = (4)/(375)`