Question

Which is the graph of f (x) = three-halves (one-third) Superscript x?

On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 1.5) and goes through (1, 1).

On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 1.5) and goes through (1, 0.5).

On a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 3) and goes through (1, 1).

Answer 1

f(x) = (3/2)·(1/3)^x.

Evaluate at x=0: f(0) = (3/2)·1 = 1.5, so it crosses the y-axis at (0, 1.5).
Evaluate at x=1: f(1) = (3/2)·(1/3) = 1/2 = 0.5.

The base 1/3 < 1 so the graph is decreasing and has horizontal asymptote y = 0. Therefore the second graph (y-intercept (0,1.5) and point (1,0.5)) is correct.