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

The second graph (y-intercept (0,4) and through (2,1)).

Reason: f(x) = 4*(1/2)^x gives f(0)=4*(1/2)^0 = 4 and f(2)=4*(1/2)^2 = 4*(1/4)=1, so the curve decays from quadrant II into I and passes through (0,4) and (2,1).