Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?
g(x) = 5(0.8)^-x
g(x) = -5(0.8)^x
g(x) = (0.8)^x
g(x) = 5(-0.8)^x

Solution:

Given f(x) = 5(0.8)^x = y

We know that (x, y) lies in Q-1

Reflection across x-axis means transforming to Q-4

In Q-4, it will be (x, -y)

So, put x = x and y = -y in given equation

5(0.8)^x = -y

-5(0.8)^x = y = g(x)

Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?

Summary:

The function represents a reflection of f(x) = 5(0.8)^x across the x-axis is g(x) = -5(0.8)^x .