Question

On a coordinate plane, 2 curves are shown. The first curve f (x) opens up and to the right in quadrant 1. It goes through (4, 2), (1, 4), and crosses the y-axis at (0, 5). The second curve g (x) opens down and to the right and goes through (4, negative 2), (1, negative 4), and crosses the y-axis at (0, negative 5).
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) = One-fifth(0.8)x
g(x) = 5(–0.8)

Answer 1

Reflection across the x-axis multiplies all y-values by −1. So the reflected function is

g(x) = −f(x) = −5(0.8)^x.

(Other choices change the exponent sign, scale by 1/5, or make the base negative — none of which are the x-axis reflection.)