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).

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, 2).

Answer 1

The second graph.

Reason: f(0) = (3/2)(1/3)^0 = 3/2 = 1.5, and f(1) = (3/2)(1/3) = 1/2 = 0.5. The base 1/3 < 1 gives exponential decay toward y = 0, so the graph crossing (0,1.5) and (1,0.5) matches option 2.