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

f(x) = (3/2)*(1/3)^x.

f(0) = (3/2)*(1) = 3/2 = 1.5, f(1) = (3/2)*(1/3) = 1/2 = 0.5. The function is an exponential decay (base 1/3 < 1) approaching y = 0 as x → ∞ and growing to the left into quadrant II.

Therefore the correct graph is the one that crosses the y-axis at (0, 1.5) and goes through (1, 0.5) — the second option.