Question

he graph shows f(x) = (one-half) Superscript x and its translation, g(x).

On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 2, 4), (negative 1, 2) and crosses the y-axis at (0, 1). g (x) decreases in quadrant 2 and approaches y = 4 in quadrant 1. It goes through (negative 2, 8), (negative 1, 6) and crosses the y-axis at (0, 5).
Which describes the translation of f(x) to g(x)?

translation of four units up
translation of five units up
translation of four units to the right
translation of five units to the right

Answer 1

Translation of four units up.

Reason: g(x) = f(x) + 4 (e.g., f(0)=1 so g(0)=5), so every y-value is 4 greater and the horizontal asymptote y=0 moves to y=4.