Question

The function f(x) = One-sixth (two-fifths) Superscript x is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?

(negative 3, StartFraction 4 Over 375 EndFraction)
(negative 2, StartFraction 25 Over 24 EndFraction)
(2, StartFraction 2 Over 75 EndFraction)
(3, negative StartFraction 125 Over 48 EndFraction)

Answer 1

Reflection across the y-axis gives g(x) = f(-x) = (1/6)*(2/5)^(-x) = (1/6)*(5/2)^x.

Alternatively, reflecting the point (3, f(3)) on f gives (-3, f(3)) on g. Compute f(3) = (1/6)*(2/5)^3 = (1/6)*(8/125) = 4/375.

So the correct ordered pair is (-3, 4/375).