Question

Which is the graph of f (x) = 3 (two-thirds) 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, 6) and goes through (1, 4).

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, 6) and goes through (1, 2).

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*(2/3)^x has f(0) = 3*(2/3)^0 = 3 and f(1) = 3*(2/3) = 2. So the correct graph is an exponential decay that crosses the y‑axis at (0,3) and goes through (1,2), and approaches y = 0 as x → ∞.

None of the three descriptions you listed matches that exactly:
- option 1: (0,6),(1,4) — wrong intercept and point;
- option 2: (0,6),(1,2) — has the correct (1,2) but wrong y‑intercept;
- option 3: (0,3),(1,1) — has the correct intercept but wrong (1,2).

So either there is a typo in the choices, or the correct choice is missing. If you must pick the closest, option 2 contains the correct point (1,2), but the y‑intercept should be (0,3), not (0,6).