Question

Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 2) and goes through (1, 5).
On a coordinate plane, an exponential function decreases from quadrant 3 to quadrant 4 and approaches y = 0 in quadrant 3. It crosses the y-axis at (0, negative 2) and goes through (1, negative 5).
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first quadrant. It goes through the y-axis at (0, 2) and goes through (negative 1, 5).
On a coordinate plane, an exponential function increases from quadrant 3 to quadrant 4 and approaches y = 0. It goes through (negative 1, negative 5) and crosses the y-axis at (0, negative 2).

Answer 1

Reflecting across the y-axis gives g(x) = f(−x) = 2(0.4)^{−x} = 2(2.5)^x, an exponential growth function with y-intercept 2.

Check points: g(0)=2, g(1)=2·2.5=5, and as x→−∞, g(x)→0 (approaches y=0 in quadrant II).

Therefore the first graph (crosses (0,2), goes through (1,5), increases into quadrant I and approaches y=0 in quadrant II) is the correct one.