Question

Which is the graph of f (x) = f (one-half) 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, 4) 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, 4) and goes through (2, 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, 2) and goes through (1, 1).

Answer 1

The middle graph (the one with y‑intercept (0,4) and passing through (2,1)).

Reason: y = 4*(1/2)^x has y‑intercept f(0)=4 and f(2)=4*(1/2)^2 = 4*(1/4)=1, so it matches the second graph. (If the intended function were just (1/2)^x, the y‑intercept would be (0,1) and none of the three graphs would match.)