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).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 fourth graph.

Reason: f(0) = 3·(2/3)^0 = 3 so the y-intercept is (0,3), and f(1) = 3·(2/3) = 2 so the graph goes through (1,2). The function is a decreasing exponential approaching y = 0, matching the fourth description.