Question

Which function represents g(x), a reflection of f(x) = On a coordinate plane, 2 exponential functions are shown. g (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1) and crosses the y - axis at (0, 0.5).(3)x across the y-axis?

g(x) = 2(3)x
g(x) = −One-half(3)x
g(x) = One-half(3)−x
g(x) = 2(3)−x

Answer 1

Reflection across the y-axis replaces x by −x. So the reflection of f(x) = (1/2)·3^x is

g(x) = (1/2)·3^(−x).

(This is the third choice: One-half(3)^{−x}.)