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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)?

User Pitos
by
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1 Answer

17 votes
17 votes

Answer:


(-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)

User Kostas Dimakis
by
2.9k points
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