Question

The function f(x) = 1/6(2/5)^x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?

a.(-3, 4/375)
b.(-2, 25/24)
c.(2, 2/75)
d.(3, -125/48)

PLEASE EXPLAIN IF YOU CAN!

Answer 1

The function f(x) = 1/6(2/5)^x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?A (-3, 4/375)- is right
B (-2, 25/24)-wrong
C (2,2/75)-wrong
D (3,-125/48)-wrong

Answer 2

(-3, 4/375)

Explanation:

Given : The function
`f(x) = (1)/(6)((2)/(5))^x` 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
`f(x) = (1)/(6)((2)/(5))^x` is reflected across the y-axis

So, we obtain a function :
`f(-x) = (1)/(6)((2)/(5))^(-x)`

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

Now substitute the given options to check which satisfies the equation.

a.(-3, 4/375)

`(4)/(375)= (1)/(6)((2)/(5))^(-(-3))`

`(4)/(375)= (4)/(375)`

Thus Option A lies on g(x)

b.(-2, 25/24)

`(25)/(24)= (1)/(6)((2)/(5))^(-(-2))`

`(25)/(24)\\eq (2)/(75)`

c.(2, 2/75)

`(2)/(75)= (1)/(6)((2)/(5))^(-(2))`

`(25)/(24)\\eq (25)/(24)`

d.(3, -125/48)

`(-125)/(48)= (1)/(6)((2)/(5))^(3)`

`(-125)/(48)\\eq (125)/(48)`

So, option A is true

(-3, 4/375) lies on g(x)