Question

The graph of f(x) = 2x is shown on the grid.

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through points (0, 1), (1, 2), (2, 4).

The graph of g(x) = (One-half)x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?

On a coordinate plane, an exponential function approaches x = 0 in quadrant 4 and increases into quadrant 1.
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and curves down into quadrant 4.
On a coordinate plane, an exponential function approaches x = 0 in quadrant 1 and curves down and to the right into quadrant 4.

Answer 1

g(x) = (1/2)^x is f(-x) (reflection of f across the y-axis). Its graph passes through (0,1), (1,1/2), (2,1/4); it is a decreasing exponential with horizontal asymptote y = 0, large as x → −∞ (in quadrant II) and → 0 as x → ∞ (in quadrant I).

Therefore choose: "On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0."