Answer:
(-3, 4/375)
Step-by-step explanation:
Given : The function [tex]f(x) = \frac{1}{6}(\frac{2}{5})^x[/tex] is reflected across the y-axis to create the function g(x).
To Find: Which ordered pair is on g(x)?
Solution:
Rule of reflection over y axis : (x,y)→(-x,y)
So, when the function [tex]f(x) = \frac{1}{6}(\frac{2}{5})^x[/tex] is reflected across the y-axis
So, we obtain a function : [tex]f(-x) = \frac{1}{6}(\frac{2}{5})^{-x}[/tex]
So, [tex]g(x) = \frac{1}{6}(\frac{2}{5})^{-x}[/tex]
Now substitute the given options to check which satisfies the equation.
a.(-3, 4/375)
[tex]\frac{4}{375}= \frac{1}{6}(\frac{2}{5})^{-(-3)}[/tex]
[tex]\frac{4}{375}= \frac{4}{375}[/tex]
Thus Option A lies on g(x)
b.(-2, 25/24)
[tex]\frac{25}{24}= \frac{1}{6}(\frac{2}{5})^{-(-2)}[/tex]
[tex]\frac{25}{24}\neq \frac{2}{75}[/tex]
c.(2, 2/75)
[tex]\frac{2}{75}= \frac{1}{6}(\frac{2}{5})^{-(2)}[/tex]
[tex]\frac{25}{24}\neq \frac{25}{24}[/tex]
d.(3, -125/48)
[tex]\frac{-125}{48}= \frac{1}{6}(\frac{2}{5})^{3}[/tex]
[tex]\frac{-125}{48}\neq \frac{125}{48}[/tex]
So, option A is true
(-3, 4/375) lies on g(x)
