Question

The graph of f(x) = (1/4)^-x is reflected about the y-axis and compressed vertically by a factor of 1/3 What is the equation of the new function, g(x)?

Answer 1

Given:

`f(x)=((1)/(4))^(-x)`

f(x) is reflected about the y-axis and compressed vertically by a factor of 1/3.

Required:

We need to find the new function g(x).

Step-by-step explanation:

The reflection of the function y=f(x) about y-axis is y=f(-x).

To reflect the given function f(x) about y-axis:

Replace x =-x in the given function f(x).

`f(-x)=((1)/(4))^(-(-x))`

`f(-x)=((1)/(4))^x`

Multiply both sides by 1/3 to get the function compressed vertically by a factor of 1/3.

`(1)/(3)f(-x)=(1)/(3)((1)/(4))^x`

The new function is

`g(x)=(1)/(3)((1)/(4))^x`

Final answer:

`g(x)=(1)/(3)*((1)/(4))^x`