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).

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, 0.5).

Answer 1

f(x) = (1/2)^x is an exponential decay with f(0)=1 and f(1)=1/2, so it crosses the y‑axis at (0,1) and goes through (1,0.5).

Among the four choices only the fourth shows the point (1,0.5), so pick the fourth graph (the decreasing curve that passes through x=1 at y=0.5).